NISTIR 8056

http://dx.doi.org/10.6028/NIST.IR.8056

Applied and Computational

Mathematics Division

Summary of Activities for Fiscal Year 2014

 

NISTIR 8056

Applied and Computational

Mathematics Division

Summary of Activities for Fiscal Year 2014

Ronald F. Boisvert, Editor

Applied and Computational Mathematics Division

Information Technology Laboratory

http://dx.doi.org/10.6028/NIST.IR.8056

April 2015

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Willie E. May, Acting Under Secretary of Commerce for Standards and Technology and Acting Director
ii NIST Applied and Computational Mathematics Division

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 eight 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 2013 through December 2014.

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

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

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

Cover Visualization: Staff in NIST’s Applied and Computational Mathematics Division are exploring 

possibilities for quantitative measurement of the magnetic moment of local iron distribution in human tissue. This distribution is suspected to be an important bio-marker for brain function and irregularities have 

been associated with traumatic brain injury. It is proposed that magnetic moments can be mapped by phase 

measurement of MRI signals. This figure shows one such measurement. The image on the left reveals a 

heavily-wrapped phase image. The linear oscillation of phase across the image is the result of an offset of 

the k-space acquisition data. Division staff members have developed an analysis which estimates and corrects for this offset. The result is shown in the image on the right. Correcting for this large systematic 

background effect will allow for more fine-scale analysis of magnetic moment distribution in the future.

See page 51.

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 Catherine Graham and Ginger White for assisting in the compilation of

Parts III and IV of this document. The word art at the start of each major section was created using Wordle 

(http://wordle.net/) to process the text of this document.

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

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

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

intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. 
Summary of Activities for Fiscal Year 2014 iii

Contents

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

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

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

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

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

Staff News............................................................................................................................................................ 8

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

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

Tamper-Resistant Cryptographic Hardware using Isolated Qubits ............................................................... 15

Computing Properties of Materials with Complex 3D Microstructures......................................................... 18

Modeling and Optimization in Cryobiology ...................................................................................................... 21

Modeling of Kinetic-based Micro Energy-Harvesters for Wearable and Implantable Sensors ................... 24

Recovery of Background Structures in Nanoscale Helium Ion Microscope Imaging .................................... 26

High Precision Calculations of Fundamental Properties of Few-Electron Atomic Systems ......................... 31

Rheology of Dense Suspensions........................................................................................................................... 34

DLMF Standard Reference Tables on Demand ................................................................................................ 38

PART III: PROJECT SUMMARIES ............................................................................................................................... 41

Mathematics of Metrology .................................................................................................................................. 43

Modeling and Optimization in Cryobiology ...................................................................................................... 43

Recovery of Background Structure in Nanoscale Helium Ion Microscope Imaging ......................................... 43

Molecular Movies: Imaging Femtosecond Motion during Electrochemical Transitions.................................. 43

A Thousand-Fold Performance Leap in Ultrasensitive Cryogenic Detectors................................................... 44

Stochastic Simulation in Chemical Spectroscopy.............................................................................................. 44

Clutter Measurements Pilot Project: Toward Evaluating Communications Spectrum Sharing Proposals .... 45

Computational Tools for Shape Measurement and Analysis............................................................................. 46

Computation of Shape Geodesics...................................................................................................................... 48

Neural Networks for Cell Feature Identification............................................................................................... 49

Stable Explicit Time Marching in Well-posed or Ill-posed Nonlinear Parabolic Equations ............................ 49

Traceable Simulation of Magnetic Resonance Imaging .................................................................................... 51

Parallel Adaptive Refinement and Multigrid Finite Element Methods.............................................................. 53

Numerical Solutions of the Time-Dependent Schrödinger Equation................................................................. 54

Equilibrium and Stability of Liquid Drops on a Conical Substrate under Gravity ........................................... 56

Modeling Magnetic Fusion................................................................................................................................ 57

Design-Basis Hurricane Winds and Missiles for Nuclear Power Plants .......................................................... 57

Algorithm Development and Uncertainty Quantification in Tomographic Radiation Transport Applications. 58

Robust and Efficient Optimization for Simulating Building Energy Usage....................................................... 59

Advanced Materials............................................................................................................................................. 61

Computing Properties of Materials with Complex 3D Microstructures............................................................ 61
iv NIST Applied and Computational Mathematics Division

Rheology of Dense Suspensions.........................................................................................................................61

Micromagnetic Modeling...................................................................................................................................61

Shear Band Formation in Bulk Metallic Glasses...............................................................................................62

Modeling of Shear Banding in Polymer Solutions.............................................................................................63

Estimation of Shear Stress in Machining...........................................................................................................64

Uncertainty Quantification and Molecular Dynamics Simulations of Aerospace Polymers .............................65

Stability of a Solid-Liquid Interface during Solidification.................................................................................66

Surface-Active Diffuse Interface Model.............................................................................................................66

Spectral-Galerkin Scheme to Study Ferroelectric Liquid Crystal Properties....................................................67

High Performance Computing and Visualization..............................................................................................70

High Precision Calculations of Fundamental Properties of Few-Electron Atomic Systems.............................70

Rheology of Dense Suspensions.........................................................................................................................70

Nano-structures, Nano-optics, and Control of Exciton Fine Structure with Electric and Magnetic Fields ......70

Modeling and Visualization of Cement Paste Hydration and Microstructure Development.............................72

New Immersive Virtual Environment.................................................................................................................74

Optical Characterization of Large Immersive 3D Displays ..............................................................................75

Texture Compression Evaluation and Optimization ..........................................................................................76

Information Visualization for Complex Information Systems............................................................................77

Visualizing the National Vulnerability Database ..............................................................................................77

WebVR Graphics................................................................................................................................................79

Quantum Information..........................................................................................................................................81

Tamper-Resistant Cryptographic Hardware using Isolated Qubits ..................................................................81

Quantum Information Science ...........................................................................................................................81

Quantum Estimation Theory and Applications..................................................................................................82

Phase Retrieval and Quantum State Tomography .............................................................................................83

Random Number Generation Based on Bell Inequality Violation .....................................................................84

Computational Complexity of Quantum Field Theory .......................................................................................85

Quantum Adiabatic Optimization ......................................................................................................................85

Quantum Computation and Knot Theory...........................................................................................................86

Post-Quantum Cryptography.............................................................................................................................87

High-Speed Error Correction Codes for Quantum Key Distribution ................................................................87

Quantum Communication ..................................................................................................................................88

Joint Center for Quantum Information and Computer Science .........................................................................91

Foundations of Measurement Science for Information Systems......................................................................92

Modeling of Kinetic-based Micro Energy Harvesters for Wearable and Implantable Sensors.........................92

An Algebraic Formulation for the Analysis and Visualization of Network Graphs...........................................92

Measuring Networks: Monte Carlo Sampling to Approximate the Chromatic Polynomial...............................93

An Improved Feedback Vertex Set Heuristic .....................................................................................................94

Extremal Theorems for Degree Sequence Packing and the 2-Color Discrete Tomography Problem ...............94

Fast Sequential Creation of Random Graphs....................................................................................................95

Identifying Important Nodes in a Network for Rapid Communication ..............................................................96

Measurement Science for Systemic Risks in Critical Infrastructures ................................................................97

Security of Complex, Interdependent Systems ...................................................................................................98

Graph Theoretic Applications to Network Security and Security Metrics.........................................................99
Summary of Activities for Fiscal Year 2014 v

Uncoordinated Scheduling Strategies for Interference Mitigation across Body Area Networks .................... 100

Combinatorial Testing..................................................................................................................................... 101

Mathematical Knowledge Management........................................................................................................... 103

DLMF Standard Reference Tables on Demand............................................................................................... 103

Digital Library of Mathematical Functions .................................................................................................... 103

Visualization of Complex Functions Data....................................................................................................... 104

Mathematical Knowledge Management .......................................................................................................... 106

NIST Digital Repository of Mathematical Formulae ...................................................................................... 107

Fundamental Solutions and Expansions for Special Functions and Orthogonal Polynomials....................... 109

PART IV: ACTIVITY DATA .................................................................................................................................. 111

Publications ........................................................................................................................................................ 113

Appeared ......................................................................................................................................................... 113

Refereed Journals ....................................................................................................................................... 113

Journal of Research of NIST ...................................................................................................................... 114

Book Chapters ............................................................................................................................................ 115

In Conference Proceedings......................................................................................................................... 115

Technical Magazine Articles...................................................................................................................... 117

Technical Reports....................................................................................................................................... 117

Accepted .......................................................................................................................................................... 117

In Review......................................................................................................................................................... 118

Invention Disclosures...................................................................................................................................... 119

Presentations ...................................................................................................................................................... 119

Invited Talks.................................................................................................................................................... 119

Conference Presentations................................................................................................................................ 121

Poster Presentations........................................................................................................................................ 124

Web Services....................................................................................................................................................... 124

Software Released .............................................................................................................................................. 124

Conferences, Minisymposia, Lecture Series, Courses..................................................................................... 125

ACMD Seminar Series..................................................................................................................................... 125

Conference Organization ................................................................................................................................ 125

Other Professional Activities............................................................................................................................. 127

Internal............................................................................................................................................................ 127

External ........................................................................................................................................................... 127

Editorial...................................................................................................................................................... 127

Boards and Committees.............................................................................................................................. 128

Community Outreach ................................................................................................................................. 129

Thesis Direction.......................................................................................................................................... 129

Awards and Recognition ................................................................................................................................... 129

Grants Awarded................................................................................................................................................. 130

External Contacts............................................................................................................................................... 130

PART V: APPENDIX .................................................................................................................................................. 133

Staff ..................................................................................................................................................................... 135

Glossary of Acronyms........................................................................................................................................ 138
vi NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2014 1

Part I: Overview

 Part I

Overview
2 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2014 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 seeks to (a) accelerate the development and deployment of information and communication 

systems that are reliable, usable, interoperable, and secure; (b) advance measurement science through innovations in mathematics, statistics, and computer science; and (c) conduct research to develop the 

measurements and standards infrastructure for emerging information technologies and applications.

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

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

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

ACMD staff members

 perform research and development in applied mathematics and 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 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 Section III of this document are organized according to these broad themes. 
4 NIST Applied and Computational Mathematics Division

Division Thematic Areas

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

models are needed to understand how to design effective 

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

analyze idealized models of physical phenomena to be 

measured, and mathematical algorithms are necessary to 

find optimal system parameters. Finally, mathematical and 

statistical techniques are needed to transform measured

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

develop fundamental mathematical methods and analytical 

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

measurement science applications. 

Advanced 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, 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 2014 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. Cryopreservation, whose goal is to preserve biological cells, tissue and organs 

by storing them at very low temperature, broadly impacts the medical and agriculture industries and has a 

growing role in forensic science. Cooling, warming and preservation strategies must be carefully designed

to avoid ice nucleation and chemical toxicity, which impact survival rates, while optimizing time and cost. 

Nevertheless, very little is actually known about the physical processes surrounding cryopreservation. In 

order to be able to develop improved protocols and measurements for such processes, Division scientists

have begun an effort to develop the foundations of mathematical modeling in cryobiology. In particular, 

they are developing a thermodynamic framework suitable for cryobiological applications, including mathematical models for thermal transport, chemical transport, mass transport and solidification processes of an 

externally-cooled ternary mixture that surrounds a biological cell. See page 21.

Successful nanoelectronics manufacturing requires high quality imaging and accurate measurements 

at the subnanometer scale. The helium ion microscope (HIM) is an important new imaging and metrology 

tool that can provide the needed accuracy. However, HIM images are often noisy, and important background structures may not be easily discernible due to the weak signal. Techniques that can overcome such 

degradations are of paramount interest. We have discovered an unexpectedly effective two-stage recovery 

and enhancement method. This involves a preliminary image-specific adaptive histogram equalization of 

the image. Such equalization enhances background information while significantly magnifying noise, and 

is not generally advisable with noisy data. However, at the second stage, an effective and easy-to-use denoising technique, based on progressive low exponent Lévy fractional diffusion smoothing, can be 

successfully applied to this histogram equalized image with magnified noise. See page 26.

The development of new algorithms and computer codes for the solution of partial differential equations (PDEs) usually involves the use of proof-of-concept test problems. Such test problems have a variety 

of uses such as demonstrating that a new algorithm is effective, verifying that a new code is correct in the 

sense of achieving the theoretical order of convergence, and comparing the performance of different algorithms and codes. Self-adaptive methods to determine a quasi-optimal grid are a critical component of the 

improvements that have been made in PDE algorithms in recent years. Although such adaptive mesh refinement techniques are now in widespread use in applications, they remain an active field of research. We 

have developed a web-based resource to provide a standard set of problems suitable for benchmarking and 

testing adaptive mesh refinement algorithms and error estimators. The development of computational 

benchmarks like this is an important component of the metrology infrastructure for scientific computing. 

See page 53.

Advanced Materials. The first 3D version of NIST’s Object-Oriented Finite Element (OOF) software, 

called OOF3D1, was released on-line in September 2014. An advanced software tool for studying the 

relationship between the microstructure of a material and its overall mechanical, dielectric, or thermal properties, the original OOF2 performed two-dimensional finite element calculations on grids derived from two 

dimensional micrographs. OOF3D performs the same task but does three dimensional calculations on three 

dimensional images, making it more directly applicable to real materials. See page 18.

 

1 The first release of OOF3D, which is numbered 3.0.0 (because the first version of OOF2 was 2.0.0), is available at 

http://www.ctcms.nist.gov/oof/oof3d.
6 NIST Applied and Computational Mathematics Division

High Performance Computing and Visualization. In a virtual measurement tour-de-force, ACMD scientists have calculated the nonrelativistic base energy levels for the four electrons in the element beryllium 

as well as the entire isoelectronic series up through atomic number 113, i.e., positive ions of all the other 

elements having the same number of electrons as beryllium2. With eight digits of accuracy, these results 

represent the most accurate computations ever done of these quantities. Years of effort have been put in to 

developing the foundational analytical and numerical machinery to solve the few-electron Schrödinger system with no approximations other than the truncation of infinite series. The four-electron case is particularly 

exciting as, due to the ACMD formalism, higher electron systems will present no new analytical difficulties.

Such a method could enable computation of other atomic properties—electron affinity and ionization potential, for example—that are important for astrophysics and other fields of atomic research. See page 31.

Recently, ACMD scientists, working with EL, the University of Strasbourg, and SIKA Corporation,

have gained fundamental insights into mechanisms that control the rheological properties of complex fluids 

like suspensions. Using their expertise in the application of high performance computers and visualization, 

along with access to DOE supercomputers, they discovered a universal law that allows one to predict the

flow behavior of hard sphere suspensions from the properties of the matrix fluid. These ideas are being 

applied to create a standard reference material (SRM 2493) for mortars, the first time a SRM was developed 

based on supercomputer simulations. Such SRMs are useful for calibration of rheometers used in research 

and development to create a new generation of products such as high performance and eco-friendly cementbased materials. See page 34.

Mathematical Knowledge Management. Special functions are fundamental tools needed for mathematical and computational modeling in the sciences and engineering. Developers of algorithms and software 

for the evaluation of special functions need a reliable source of function values in order to test their implementations. While many libraries or systems efficiently produce function values, few offer any information 

about the accuracy of their computations. To fill this need, we are working with colleagues at the University 

of Antwerp to provide users of the NIST Digital Library of Mathematical Functions (DLMF) the ability to 

generate tables of special functions on demand whose accuracy is carefully controlled, and whose results 

come with a reliable statement of uncertainty. A prototype of the DLMF “Live Tables” has been completed 

and is currently accessible online. See page 38.

We have taken a major step in improving the accessibility of the 3D interactive graphics in the Digital 

Library of Mathematical Functions (DLMF) with the release of DLMF Version 1.07 in March 2014. Previously these graphics were rendered using two common technologies, VRML and X3D, which require 

users to download a plugin based on their operating system. Not only is this inconvenient for users, it poses 

difficulties for those maintaining the site, since updates of the plugin, web browser, and even the operating 

system can affect the quality of the visualization. To remedy this problem we converted the DLMF 3D 

graphics to a recently available standard format, WebGL. WebGL visualizations are visible on Windows, 

Mac, and Linux platforms in most HTML5 compatible browsers. See page 104.

Quantum Information. One-time memories are a basic primitive for constructing more general cryptographic tools, such as one-time programs. One-time programs could enable construction of electronic 

tokens or electronic cash, or enable certain forms of software protection. ACMD has developed a new 

theoretical construction for one-time memories based on isolated qubits. (Isolated qubits are a special class 

of quantum devices, which have long coherence times, but do not allow entangling operations. These may 

be realizable in well-studied quantum systems such as solid-state nuclear spins.) These results demonstrate,

for the first time, that quantum-based one-time memories can achieve several of the basic requirements for 

use in cryptographic applications. See page 15.

Many applications of quantum mechanics to communication and cryptography rely on experimental 

tests of Bell inequalities. These tests also provide the strongest evidence against local realism (LR) as a 

possible explanation of quantum non-determinism. While there have been many experiments demonstrating 

the required violation of Bell inequalities, so-far they have suffered from loopholes and problems with 

 

2 Electron energy levels also depend on relativistic and quantum electrodynamic effects caused by the atom's nucleus, but they're negligible until 

you get to higher atomic number atoms.
Summary of Activities for Fiscal Year 2014 7

quantifying the evidence against LR. ACMD mathematicians have developed a powerful strategy for analyzing Bell-test data that can quantify the evidence against LR in a configuration-independent way. They 

have applied this method to Bell-test data from the University of Illinois to show that it violates LR without 

being subject to the so-called detection loophole. A conventional analysis did not show this violation. Such 

analyses will be critical to the success of the NIST Innovations in Measurement Science Project Quantum 

Randomness as a Secure Resource, which aims to provide random bits to the NIST Randomness Beacon 

guaranteed by the laws of physics to not have been known before measurement. See pages 81 and 84.

Finally, this year we helped establish the Joint Center for Quantum Information and Computer Science 

(QuICS), which was formally inaugurated on October 31, 2015. A collaborative venture of NIST, the 

University of Maryland and Research Directorate of the National Security Agency/Central Security Service, QuICS will conduct basic research to understand how quantum systems can be effectively used to 

store, transport and process information. The work of QuICS will be carried out jointly by staff of the 

participating institutions, as well as by graduate students, postdocs, and visiting scientists. See page 91.

Foundations of Measurement Science for Information Systems. RF-enabled wearable sensors offer an 

attractive set of e-health applications, among which are monitoring of temperature, respiration, heart rate, 

and blood pressure. As these sensors are small and mainly rely on very small batteries to carry out their 

functions, prolonging their operational lifetime could significantly help their commercial applications. We 

are investigating the feasibility of capturing and storing kinetic energy from human body motion to power 

such devices. To do this we have developed a statistical model of acceleration generated as a result of 

typical human motion, modeled a micro-harvester device suitable for wearable/implantable applications, 

and modeled and characterized the instantaneous power that can be generated by the device. See page 24.

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 42 articles appearing in peer-reviewed journals and 35 papers in conference proceedings. Fifteen additional papers have been accepted for publication, while 43 others are undergoing review. 

Division staff gave 50 invited technical talks and presented 50 others in conferences and workshops. 

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

notably the Digital Library of Mathematical Functions, though legacy services no longer actively maintained, like the Guide to Available Mathematical Software, the Matrix Market, and the SciMark Java 

benchmark still see significant use. During calendar year (CY) 2014, the division web server satisfied more 

nearly 5 million requests for pages during more than 1.1 million user visits. In total, there have been more 

than 371 million “hits” on ACMD Web servers since they went online as NIST’s first web servers in 1994. 

Another indication of the successful transfer of our technology is references to our software in refereed 

journal articles. For example, our OOMMF software for nano-magnetic modeling was cited in 167 such

papers published in CY 2014 alone. 

Members of the Division are also active in professional circles. Staff members hold a total of 19

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 31 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:

 Bell Labs-NIST Workshop on Large-Scale Networks3. Murray Hill, NJ. October 25, 2013. Murray 

Hill, NJ. (Vladimir Marbukh, Co-Organizer)

 Workshop on Uncertainty Quantification in Materials Modeling4, Institute for Mathematics and 

Its Applications, University of Minnesota. December 16-17, 2013. (Andrew Dienstfrey, Co-Organizer)

 

3

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

4

http://www.ima.umn.edu/2013-2014/SW12.16-17.13/?event_id=SW12.16-17.13
8 NIST Applied and Computational Mathematics Division

 UMD-NIST Symposium on Network Science. University of Maryland. January 24, 2014. (Assane 

Gueye, Co-Organizer)

 NIST-UMD Workshop on Quantum Information and Computer Science5. University of Maryland. 

March 31 – April 1, 2014. (Stephen Jordan and Yi-Kai Liu, Co-Organizers)

 Third International Workshop on Combinatorial Testing6. Cleveland, OH. March 31, 2014. 

(Raghu Kacker and Yu Lei, Co-Organizers)

 IEEE 25th Annual Conference on Personal, Indoor and Mobile Radio Communications

(PIMRC)

7

. Washington, DC. September 2-5, 2014. (Kamran Sayrafian, Principal Organizer and 

Chair of the Technical Program Committee)

 Workshop on Dynamics of and on Networks8. Santa Fe Institute, NM. December 1-5, 2014. (NIST 

grant provided partial funding for this event.)

Plans are underway for several major events in the coming year:

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

(OPSFA)9. NIST, Gaithersburg, MD. June 1-5, 2015. (Daniel Lozier, Co-Organizer and Howard 

Cohl, Member of the Program Committee).

 Conference on Intelligent Computer Mathematics (CICM)10. Washington, DC. July 13-17, 2015. 

(Bruce Miller and Abdou Youssef, Co-Organizers)

 Workshop on Uncertainty Quantification in Materials Modeling11, Purdue University, West Lafayette, IN. July 28-31, 2015. (Andrew Dienstfrey, Co-Organizer)

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

is serving as Vice-Chair and Chair-Elect of the Division of Computational Physics of the American Physical 

Society (APS). Geoffrey McFadden was elected to the position of 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 Information Technology Research and Development 

(NITRD) Program. 

For further details, see Section IV, Activity Data.

Staff News

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

Arrivals

Yvonne Kemper began a stay in ACMD as a NIST National Research Council (NRC) Postdoctoral Associate in December 2013. She received a Ph.D. in mathematics from the University of California at Davis in 

2013, where she wrote a thesis on structural measurements of simplicial complexes and convex polytopes.

 

5 http://www.nist.gov/itl/math/quics-workshop.cfm

6

http://www.research.ibm.com/haifa/Workshops/iwct2014/program.shtml

7

http://www.ieee-pimrc.org/2014/

8

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

9

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

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

11 http://www.ima.umn.edu/2014-2015/SW7.28-31.15/
Summary of Activities for Fiscal Year 2014 9

At NIST she has been working with Isabel Beichl on approximating the chromatic polynomials of largescale networks. 

Barry Schneider, a long-time Program Manager in the Division of Physics at the National Science Foundation, as well as a NIST Guest Researcher, began a full-time appointment in ACMD in January 2015 as 

one of the principals in the NIST Digital Library of Mathematical Functions project. An expert in computational physics and high performance computing, Schneider will also contribute to ACMD work in these 

areas.

Michael Mascagni, a Professor of Computer Science at Florida State University, began a faculty appointment in ACMD in late FY 2013. He is spending the 2014-15 academic year on sabbatical at NIST. An 

expert in high performance computing and Monte Carlo methods, Mascagni is focusing on applications in 

materials modeling at NIST.

Departures

Sean Colbert-Kelly completed his term as a NIST/NRC Postdoctoral Associate in ACMD September 

2014. He went on to a position at Noblis, a non-profit science and engineering think-tank in the Washington, 

DC area. At NIST Colbert-Kelly developed and analyzed models of surfactants and ferro-electric liquid 

crystals. He continues as a NIST guest researcher.

In July 2014 Michael Cromer completed his term as an NIST/NRC Postdoctoral Associate, assuming the

position of Assistant Professor in the Mathematical Sciences Department at the Rochester Institute of Technology. At NIST Cromer worked with Geoffrey McFadden on models of shear banding in polymer 

solutions.

Daniel Kaslovsky, recipient of an NSF Postdoctoral Fellowship for Transformative Computational Science 

using CyberInfrastructure, who was carrying out his research in ACMD in Boulder, accepted a permanent 

position at Seagate Technology in Longmont, Colorado. 

Students

During FY 2014 ACMD was able to support the work of 39 student interns, including 11 graduate students, 

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

Figure 1. Some of ACMD’s summer interns. From left to right: Jimmy Li (Richard Montgomery High School), Alex Danoff (Wootton High 

School), Jessie Hirtenstein (American University), Wenqing Xu (Montgomery Blair High School), David Gunby (Georgetown Day School), Justin 

Oh (Brown University), Brandon Alexander (UMBC).
10 NIST Applied and Computational Mathematics Division

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 127.

Table 1. Student Interns in ACMD

Name Institution Type Mentor Project 

Brandon Alexander UMBC U SURF H. Cohl MediaWiki Extension Development for Digital 

Repository of Mathematical Formulae.

Sharan Arkalgud Thomas Jefferson H.S. for 

Science andTechnology

HS Vol S. Langer Image Processing Algorithms Implementation

Kathleen Arnett Richard Montgomery 

High School

HS Vol H. Cohl Digital Repository of Mathematical Formulae

Hazma Attak G FGR J. Terrill Visualization with D3

Martina Barbi University of Bologna G FGR K. Sayrafian Dynamic channel modeling in body area networks

Michael Baume University of Maryland G DGR S. Jordan Mathematical analysis of quantum algorithms

Earl Bellinger SUNY Oswego G NPSC J. Terrill Data mining

Styvens Belloge ISIMA G FGR J. Terrill Visualization and analysis of the National Vulnerability Database

Luis Catacora University of Maryland U SURF J. Terrill Visualization with D3

Faical Congo ISIMA G FGR S. Langer Software development for the OOF materials 

modeling system

Theodore Corrales Montgomery Blair H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae

Alex Danoff Thomas S. Wooton H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae

Romain Desaymons ISIMA G FGR J. Terrill Parallelization of Hydratica

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

Behnaz Ghouchani City College of NY U SURF B. Schneider Exponential time differencing methods.

Mohamed Gueye City College of NY U SURF S. Ressler Web based information visualization.

David Gunby Georgetown Day H.S. HS SVP F. Hunt Communication in engineering

Jessica Hirtenstein American University U SURF H. Cohl Orthgonal polynomials and special functions.

Kim Jablonski Jacobs Univeristy Bremen U FGR B. Miller Mathematical Knowledge Management

Adam Keith University of Colorado U PREP E. Knill Quantum information theory

Lucianna Kiffer Tulane University U SURF S. Langer Software development for the OOF materials 

modeling system

Lukas Kohlhase Jacobs Univeristy Bremen U FGR B. Miller Mathematical knowledge management

Nadav Kravitz University of Maryland U SURF S. Glancy Quantum state estimation

Jimmy Li Richard Montgomery H.S. HS SHIP H. Cohl Media Wiki Extensions

Amber Liu Poolesville H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae

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

Jacob Migdall Poolesville H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae

Azeem Mohammed Poolesville H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae 

Sung-Ho Oh Brown University U SURF F. Hunt Spreading information, consensus in a network

Ayotunde Olutade Jackson State University U SURF J. Terrill Visualization with D3

Alicia Ouyang River Hill H.S. HS SHIP J. Terrill D3 visualization of HydratiCA Data

Jane Pan University of Maryland U SURF S. Langer Detecting geometry and structure in images

Moritz Schubotz Technische Universitaet 

Berlin

G FGRR

S

H. Cohl MediaWiki Extension development for the Digital Repository of Mathematical Formula

Diamond Smith Charles H. Flowers H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae

James van Meter University of Colorado G PREP E. Knill Relativistic quantum information

Michael Vetter Poolesville H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae

Peter Wills University of Colorado G PREP E. Knill Statistical analyses for quantum information

William Xu Montgomery Blair H.S. HS SVP H. Cohl q-hypergeometric orthogonal polynomials

Cherry Zou Poolesville H.S. HS SVP H. Cohl Digital Repository of Mathematical Formulae 

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

U Undergraduate FGR Foreign Guest Researcher

HS High school NPSC National Physical Sciences Consortium Fellow

NSF National Science Foundation Fellow

DGR Domestic Guest Researcher

SURF Summer Undergraduate Research Fellowship

SHIP Summer High school Internship Program

SVP Student Volunteer Program
Summary of Activities for Fiscal Year 2014 11

Recognition

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

below.

Manny Knill was selected to receive one of twelve 2013 Arthur Flemming Awards. Administered 

by the Trachtenberg School of Public Policy and Public Administration of George Washington University, 

the Flemming Award honors outstanding men and women in the Federal service. At the June 2014 ceremony in Washington, DC, Knill was recognized as “one of the world’s leading theorists in the field of 

quantum information science and engineering.”

Ronald Boisvert was selected to receive the 2014 

Award in Mathematics and Computer Science from the 

Washington Academy of Sciences (WAS). The award 

was conferred during ceremonies held at the Sphinx 

Club in Washington, DC on May 8, 2014. Awardees are 

also recognized as Fellows of the WAS.

Jeffrey Fong has received the 2014 Lifetime 

Achievement Award from the International Conference 

on Computational Engineering and Science (ICCES). 

Fong was cited for his “seminal contributions to reliability engineering and probabilistic mechanics.” The 

ICCES Lifetime Achievement Award recognizes sustained and significant contributions in the form of 

research, teaching, and service to the community, in the 

technical areas of the ICCES series of conferences. The 

award ceremony took place on June 16, 2014 during the 

ICCES conference in Changwon, Korea. 

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 101. D. Richard Kuhn of the ITL Computer Security Division was a joint honoree.

A portrait of Jack Edmonds was enshrined in 

the NIST Gallery of Distinguished Scientists, Engineers and Administrators in ceremonies held at the 

NIST Gaithersburg Laboratories on October 10, 

2014. Administered by the Standards Alumni Association, the gallery honors former NIST staff 

members who made outstanding contributions during 

their tenure here. Edmonds was recognized for “prolific and fundamental contributions in combinatorial 

optimization and discrete mathematics.” He was one 

of the creators of the fields of combinatorial optimization and polyhedral combinatorics, which emerged 

during the period of his tenure at NIST from 1959-

69. In addition, Edmonds produced many deep and 

important theoretical results in matroid theory. His 

contributions also helped pave the way for modern

computational complexity theory. He was the first to 

describe the complexity class NP, to describe a tractable computation as one that is solvable in 

polynomial time, and to state the now widely held 

conjecture that the complexity classes P and NP are 

Figure 2. Charles Romine, Director of the NIST Information 

Technology Laboratory, presents the Washington Academy of 

Sciences Award in Mathematics and Computer Science to 

Ronald Boisvert.

Figure 3. Jack Edmonds delivers remarks at the 2014 Alumni Portrait Gallery Ceremony.
12 NIST Applied and Computational Mathematics Division

not equivalent. For futher details, see the account of Sipser published in the 1992 Proceedings of the ACM 

Symposium on the Theory of Computing12. 

Chris Schanzle received the Outstanding Service Award from the NIST Chapter of Sigma Xi, the 

Scientific Research Society. Schanzle was cited for his “exceptional service in support of the ITL Applied 

and Computational Mathematics Division (ACMD), the Statistical Engineering Division (SED), and their 

collaborators ... which enables state-of-the-art computational science in support of the NIST Laboratory 

programs.” 

ACMD staff members and associates garnered three of the six annual ITL awards presented in 2014:

 Outstanding Contribution to ITL: Bruce Miller. For technical excellence in development of the 

computational infrastructure underlying the NIST Digital Library of Mathematical Functions.

 Outstanding Journal Paper: Yanbao Zhang, Scott Glancy and Manny Knill, Efficient Quantification of Experimental Evidence against Local Realism, Physical Review A 88, 052119.

 Outstanding Technical Support: Chris Schanzle. (Joint Award) For extraordinary leadership and 

dedication to users in securing the ITL computing environment through the upgrading of systems 

for secure BIOS and Windows 7.

Finally, ACMD Administrative Assistant Ginger White completed her studies at the University of 

Maryland in December 2013 and was awarded a Master’s in Business Administration.

 

12 http://dx.doi.org/10.1145/129712.129771
Summary of Activities for Fiscal Year 2014 13

Part II: Features

 

 Part II

Features
14 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2014 15

Tamper-Resistant Cryptographic Hardware using Isolated 

Qubits

Tamper-resistant cryptographic hardware is used to 

protect information that is stored in devices that are under the physical control of an adversary. For instance, 

tamper-resistant hardware can prevent a thief from 

reading private data from a stolen smartphone, or making unauthorized copies of movies from a streaming 

video player. In these situations, while the data may be 

protected by encryption, an adversary can circumvent 

this protection by finding the secret keys that are used to 

decrypt the data; these keys must be present somewhere 

in the device while it is running. Tamper-resistant hardware can prevent an adversary from reading these 

secret keys, and can disable the device if it is accessed 

improperly.

Designing tamper-resistant hardware is a difficult 

task. One would like to design devices whose security 

follows directly from the laws of physics. Alas, neither 

classical nor quantum physics seems capable of providing such guarantees. Nevertheless, we have discovered 

a conceptually elegant approach to solving this problem, using a special class of quantum mechanical 

devices called isolated qubits. Using this approach, we 

provide theoretical constructions of cryptographic 

primitives called one-time memories, as well as tamperresistant “black boxes” called one-time programs.

Yi-Kai Liu

Originally proposed by Shafi Goldwasser, Yael Tauman 

Kalai and Guy Rothblum in 2008 [1], a one-time program is a program that can be run exactly once. After the 

program has run, it stops working, and “self-destructs.” 

In addition, the program reveals nothing about its internal operation; thus it behaves like an oracle, or “black 

box.” One-time programs are a simple but powerful 

form of software protection and access control. They are 

convenient objects for theoretical investigation, which 

are applicable (at least in principle) to a wide range of 

security problems. For example, a one-time program can 

provide access to encrypted data, without revealing the 

decryption keys, and while limiting the amount of data 

that can be decrypted.

Goldwasser, Kalai and Rothblum showed that onetime programs can be constructed from simpler devices 

called one-time memories. A one-time memory stores 

two (pre-programmed) messages, and allows a user to 

read either of the messages, but not both of them. Thus, 

a one-time memory is equivalent to a one-time program 

that only takes a single bit of input. One-time memories 

are simpler to construct than one-time programs, because they only perform table lookups, rather than 

arbitrary computations.

We would like to construct one-time memories 

whose security is guaranteed by basic principles of 

physics. In particular, we desire information-theoretic 

security, which holds against adversaries with unlimited 

computational power. However, this turns out to be impossible using classical physics. In classical physics, 

information can always be copied, at least in principle, 

and so at a fundamental level, there is no way to prevent 

the adversary from duplicating the entire one-time 

memory, and then reading one message from the original memory and the other message from the duplicate 

memory – thus breaking the security guarantee. 

In quantum physics, things seem more promising, 

because of surprising phenomena that occur when information is encoded in superpositions of quantum states. 

In particular, the no-cloning theorem guarantees that an 

unknown quantum state cannot be copied. But in fact, 

this is not sufficient for our purposes. There are general 

“no go” theorems in quantum cryptography, discovered 

around 1996 by Dominic Mayers, Hoi-Kwong Lo and 

H. F. Chau [5-7], which show that any construction for 

quantum bit-commitment or oblivious transfer can be 

broken by performing measurements that use entanglement. (We will say more about entanglement later.) 

These results imply the impossibility of one-time memories using quantum physics.

Something different is needed, then, in order to construct one-time memories. We show that this can be 

done using a special class of quantum devices, called 

isolated qubits. These are qubits that can only be accessed using a special subset of quantum operations, 

known as local operations and classical communication, or LOCC. Intuitively, these are quantum operations 

Figure 4. An adversary who has physical access to a device can 

read all of the data stored on it, including secret keys used for encryption and decryption. Tamper-resistant hardware provides a 

solution to this problem.
16 NIST Applied and Computational Mathematics Division

on single qubits, combined with classical control signals 

between the qubits.

To understand the properties of isolated qubits, it is 

helpful to think in terms of entanglement. Roughly 

speaking, quantum entanglement is a special kind of correlation between particles, which is stronger than that 

allowed in classical physics. Quantum entanglement is a 

powerful resource for communication and computation. 

It plays an essential role in quantum teleportation, and 

quantum algorithms for factoring large numbers in polynomial time. Yet entangled quantum states are also 

fragile, and easily damaged by interactions with their 

surrounding environment. To work with these entangled 

states, quantum computers have to perform elaborate error correction procedures.

Isolated qubits can only be accessed using LOCC 

operations, which cannot generate entanglement. Indeed, isolated qubits are designed so that it is impossible

to prepare entangled states, or perform entangling operations. This is much easier than building a quantum 

computer; indeed, there are natural physical systems, 

such as solid-state nuclear spins, that have these properties. Moreover, it turns out that the absence of 

entanglement can be useful for cryptography. One can 

design protocols where an honest user does not need entanglement in order to participate, but a dishonest user 

needs entanglement in order to cheat (reminiscent of the 

“no go” theorems mentioned previously). This, roughly 

speaking, is how our one-time memories work.

More precisely, our one-time memories use an idea 

called conjugate coding, which was first proposed by 

Stephen Wiesner in the 1970s [8]. The basic idea is to 

encode two classical bits, a and b, into a single qubit, 

such that by performing different kinds of measurements 

on the qubit, one can gather information about either a

or b (see Figure 5). One cannot reconstruct a or b perfectly; one can only guess the correct value with 

probability ≈ 0.85. However, by extending this idea to 

use a classical error-correcting code and multiple qubits, 

one can get a scheme that allows either a or b to be reconstructed reliably. This will be our candidate for a 

one-time memory.

The above scheme uses multiple qubits, and so the 

question naturally arises: what happens if one performs 

entangling operations on them? Wiesner pointed out that 

one can actually learn both of the messages a and b in 

this way. Using entangling operations, one can run the 

decoding procedure in superposition, and thereby learn 

a without damaging the quantum state; one can then repeat this procedure to learn b. This attack would break 

the security of our scheme. 

Fortunately, we are able to avoid this problem, by 

building our one-time memories out of isolated qubits, 

where entangling operations are simply impossible. 

(One can check that our scheme still works correctly using isolated qubits, as the honest parties only need to 

perform LOCC operations.) 

We then prove that these one-time memories are secure: we show that any adversary who performs only 

LOCC operations cannot learn both a and b, i.e., entanglement is necessary in order to break the security of this 

scheme. This is the main technical contribution of our 

work [2-4]. 

The proof requires several ingredients. The choice 

of a suitable error-correcting code is crucial for security 

and efficiency; we get good results by using a particular 

class of codes that are linear over GF(2), approach the 

capacity of the q-ary symmetric channel, and are efficiently decodable. We prove security using a high-order 

entropic uncertainty relation, which was originally devised for quantum cryptography in the bounded storage 

model. To complete the proof, we use a novel form of 

privacy amplification, with a fixed (deterministic) hash 

function that may be known to the adversary beforehand; this is needed because one-time memories are 

non-interactive, in contrast to interactive protocols such 

as quantum key distribution.

This result is an important step in a broader research 

project, whose goal is to build one-time programs (and 

other kinds of tamper-resistant hardware) whose security is based on physical principles. This project can be 

organized around different levels of abstraction:

1. Physical devices, e.g., solid-state nuclear spins.

Figure 5. One possible implementation of conjugate coding. A single qubit is prepared in one of four possible states |ψab⟩, which 

encode two classical bits a and b; these states are represented by 

two-dimensional vectors, drawn in green. To gather information 

about the bit a, one performs a measurement in the horizontal/vertical basis, represented by the vectors |θ0

⟩ and |θ1⟩, drawn in 

black. This measurement returns an outcome m, which may be either 0 or 1, with probability |⟨θm|ψab⟩|

2

, that is, the square of the 

inner product of |ψab⟩ and |θm⟩. One can check that m = a with 

probability cos2(π/8) ≈ 0.85. To gather information about the bit b, 

one performs a measurement in the diagonal basis, represented by 

the vectors |θ0′⟩ and |θ1′⟩, drawn with dashed lines. This measurement returns an outcome m, such that m = b with probability 

cos2(π/8) ≈ 0.85.
Summary of Activities for Fiscal Year 2014 17

2. Isolated qubits: a mathematical model of the 

physical devices.

3. One-time memories: cryptographic primitives 

built from isolated qubits.

4. One-time programs: general functionalities built 

from one-time memories.

Thus far, we have mainly studied constructions for 

one-time memories using isolated qubits. The next step 

will be to develop experimental implementations of isolated qubits, keeping in mind that real physical devices 

are never a perfect match for their idealized mathematical descriptions. Another step will be to understand the 

security issues that arise when many one-time memories 

are linked together to form one-time programs (“composable security”). Ultimately, by putting together all of 

these pieces, we hope to obtain a more rigorous methodology for building tamper-resistant cryptographic 

hardware.

References

[1] S. Goldwasser, Y. T. Kalai and G. N. Rothblum, OneTime Programs, in Proceedings of CRYPTO 2008, 39-56.

[2] Y.-K. Liu, Privacy amplification in the isolated qubits 

model, in Proceedings of EUROCRYPT 2015, to appear.

[3] Y.-K. Liu, Single-shot Security for One-time Memories 

in the Isolated Qubits Model, in Proceedings of CRYPTO 

2014, Part II, 19-36.

[4] Y.-K. Liu, Building One-Time Memories from Isolated 

Qubits, in Proceedings of Innovations in Theoretical 

Computer Science (ITCS) 2014, 269-286.

[5] H.-K. Lo and H. F. Chau, Is Quantum Bit Commitment 

Really Possible? Physical Review Letters 78 (1997), 

3410.

[6] H.-K. Lo, Insecurity of Quantum Secure Computations, 

Physical Review A 56:2 (1997), 1154-1162.

[7] D. Mayers, Unconditionally Secure Quantum Bit Commitment is Impossible, Physical Review Letters 78

(1997), 3414-3417.

[8] S. Wiesner, Conjugate Coding, ACM SIGACT News, 15:1 

(1983), 78-88. (Original manuscript written circa 1970.)

Participants

Yi-Kai Liu (ACMD)
18 NIST Applied and Computational Mathematics Division

Computing Properties of Materials with Complex 3D

Microstructures

Many macroscopic properties of materials, such as 

strength, hardness and corrosion resistance are dependent upon microstructure, the complex arrangement of 

material components visible only under a microscope.

Material scientists wish to understand the mechanisms 

by which microstructure influences macroscopic properties, with the ultimate goal of designing new materials 

with particular microstructures in order to obtain desired properties. We have been developing software to 

enable matrial scientists to model such systems starting 

with an image of the microstructure. Previous versions

of the software, OOF1 and OOF2, did two dimensional

calculations on two dimensional images. By moving into 

three dimensions, OOF3D makes the calculations more 

directly relevant to real materials.

Stephen Langer

The OOF Project is a long running collaboration between the Applied and Computational Mathematics 

Division and the NIST Material Measurement Laboratory to model the properties of materials with complex 

microstructures. Such materials have complicated structure on scales larger than the atomic scale, but smaller 

than the macroscopic, everyday, scale. Metals are common examples. They are often composed of assemblies 

of grains, each of which is a single crystal, but which is 

oriented differently from its neighbors. The exact arrangement of the microscopic orientations can affect the 

macroscopic properties of the material. Ceramics are another example, often being composed of microscopic

crystalline grains embedded in an amorphous matrix. 

Biological materials also often have complex microstructures. Bone appears to be a solid at large length 

scales, but is microscopically revealed to have an intricate porous structure. Artificial materials can also be

constructed with complex microstructures by weaving, 

laminating, or etching.

Modeling a material mathematically or computationally gives researchers insights into why the material 

behaves the way that it does, and allows them to predict 

ways in which the material properties might be improved. There are two general schemes for modeling

microstructures. The first is to assume that the randomness and complexities in the microstructure can be 

averaged out in a homogenization procedure. The second is to perform a brute force computation of the 

properties of a particular configuration of the microstructure and to examine in detail how that particular 

instance behaves. The first method has the advantage 

that it can be applied to large systems and can in some 

cases lead to analytical results. On the other hand, homogenization discards information and cannot compute

effects that depend upon the less probable (but still extant) features of a microstructure. For a simple example, 

consider a material made of two components with very 

different thermal conductivities. The thermal conductivity of the bulk material will depend on whether or not 

the high conductivity regions can be joined together to 

form a continuous path from one side of the sample to 

another. A homogenization method that assumes a regular repeating structure is unlikely to compute the 

correct bulk conductivity. A brute force computation 

won’t compute the correct average behavior (even if the

word “average” can be well defined) but repeated brute 

force calculations will compute the correct result for 

particular samples, and give insight into their statistical 

distribution.

OOF is a tool for brute force computations of the 

properties of microstructures. Using it, a researcher 

starts with a real or simulated image of a microstructure, 

assigns material properties to the features of the image, 

constructs a finite element mesh, and solves the relevant 

physics equations for the properties of interest. The solution can be viewed at the microscopic level, or 

averaged over the whole system to compute its effective 

macroscopic properties. OOF solves a wide variety of 

linear and nonlinear problems in elasticity, polarization, 

and thermal conductivity, including couplings such as

piezoelectricity and thermal expansion.

The OOF project began in the late 1990’s with 

OOF1, which was written in C++ and could only solve 

two dimensional static elasticity and thermal conductivity systems. OOF2, which was a complete rewrite of

OOF1 in a combination of C++ and Python, improved 

OOF’s modularity enormously and added the ability to 

solve time-dependent systems, but was still restricted to 

two dimensions. OOF3D, which was released this past 

year, does almost everything that OOF2 can do, but does 

it in three dimensions. There were two reasons for limiting OOF1 and OOF2 to two dimensions: at the time 

there were few experimental methods for obtaining detailed 3D microstructures, and 2D calculations are 

substantially easier than 3D ones. The situation has 

changed, and now there are many techniques being used 

to get 3D microstructural data [1], so there is a need for 

a 3D version of OOF.

Migrating from two to three dimensions has been a 

multi-year effort. The basic control structures and 

graphical user interface used in OOF2 survives unchanged in OOF2, with the exception of the code for

displaying microstructures and meshes, which had to be 

completely replaced. Both programs use PyGTK [2] for 
Summary of Activities for Fiscal Year 2014 19

user interface components (menus, buttons, and other 

widgets), but OOF2 uses the Gnome canvas [3] for displaying two dimensional images and other graphical 

objects, while OOF3D uses the VTK [4] visualization 

toolkit. Using VTK efficiently required modifying 

some of OOF2's methods for storing and manipulating 

images and meshes, but most of the code for setting up

and solving equations could be transferred virtually unchanged from OOF2 to OOF3D. (The exceptions were 

the boundary condition code, which had to be extended 

to handle two dimensional boundaries, and the OOF2 

code for handling plane-stress, plane-strain, and their

generalizations, which had to be eliminated.)

Using either OOF2 or OOF3D involves the following steps.

1. Load an image and assign material properties to its 

features. For example, each pixel (or voxel, in 3D) 

could be given a particular elasticity modulus and 

crystal orientation. Figure 6 is a small sample from 

a micrograph of bone, showing that it is constructed 

from two different materials on the microscale.

2. Superimpose a uniform mesh on the image. In 2D, 

this can be either a triangular or quadrilateral mesh. 

In 3D, it must be tetrahedral (for now).

3. Modify the mesh so that it is a good representation 

of the image, by moving nodes and subdividing (refining) elements. (Figure 7 shows an OOF3D mesh 

adapted to the image in Figure 6. Elements from 

only one material are filled in.) OOF provides a 

number of mesh modification tools. Ideally, after 

the mesh is modified all of the pixels within every 

mesh element will have the same material properties as the other pixels within that element; that is, 

the ideal element will be homogeneous. The OOF2 

and OOF3D mesh modification tools use the homogeneity as part of an element fitness function, and it 

is important that the function be a continuous function of the mesh node positions. To make the 

homogeneity continuous, the program needs to 

compute the fractional area or volume of pixels 

through which an element edge passes. This calculation is the most CPU intensive part of the 3D mesh 

construction process and is one of the biggest under-the-hood differences between OOF2 and 

OOF3D.

4. Define which fields (temperature, displacement, 

etc.) will be defined on the mesh, and which equations (force balance, heat flow, etc.) will be solved. 

These must be consistent with the material properties assigned to the image.

5. Set boundary conditions and initial values.

6. Choose a solver and solve the equations. OOF2 offers a number of different solution methods, but 

Figure 6. Small sample from a micrograph of bone, showing that 

it is constructed from two different materials on the microscale.

Figure 7. An OOF3D mesh adapted to the image above.

Figure 8. Example result from a computational simulation run using the mesh above.
20 NIST Applied and Computational Mathematics Division

also has a “Basic” mode which makes reasonable 

default choices for non-expert users.

7. Visualize the results and compute output quantities. 

Figure 8 demonstrates a possible solution on the 

bone sample from Figure 6. The two materials have 

been given different thermal conductivities and a 

temperature gradient has been imposed on the sample. The colors indicate the local value of the heat 

flux. (Because the input conductivities and the 

boundary conditions were arbitrarily chosen for this 

example, the actual values of the outputs aren’t 

meaningful.)

Development continues on both OOF2 and 

OOF3D. Future work will allow the programs to compute more physical properties, particularly plasticity and 

surface effects. Both programs can benefit from parallel 

processing, and OOF3D will get more flexible methods 

for user interaction.

OOF3D can be downloaded from NIST (see below). It runs only on Linux and Macintosh OS X 

systems, although it can be used inside a Linux virtual 

machine on Windows.

References

[1] A. P. Cocco, et al. Three-dimensional Microstructural 

Imaging Methods for Energy Materials, Physical Chemistry Chemical Physics 15 (2013), 16377.

[2] http://www.pygtk.org/

[3] https://developer.gnome.org/libgnomecanvas/stable/GnomeCanvas.html

[4] http://www.vtk.org/

Participants

Stephen Langer (ACMD), Gunay Doğan (Theiss Research), Yannick Congo (ISIMA) and Andrew Reid 

(NIST MML).

http://www.ctcms.nist.gov/oof/

http://www.ctcms.nist.gov/oof/oof3d
Summary of Activities for Fiscal Year 2014 21

Modeling and Optimization in Cryobiology 

Cryopreservation, whose goal is to preserve biological 

cells, tissue and organs by storing them at very low temperature, broadly impacts the medical and agriculture 

industries and has a growing role in forensic science. In 

the field of cryobiology, which sits at the intersection of 

biology, chemistry and physics, mathematical and computational science plays an increasing and crucial role 

in establishing, investigating and interpreting approximate models that can be used to predict and control 

complex processes. Optimization techniques applied to 

these computational models allow cryobiologists to develop effective and efficient cooling and warming 

protocols that can be applied to biological specimens in 

practice. Our work has been directed towards this problem on numerous fronts. First, we have developed first 

principle models of thermal, chemical and mass 

transport in cryobiological systems. These mathematical models take the form of coupled partial differential 

equations with multiple moving boundaries representing (solid-liquid) phase boundaries and semi-permeable 

cellular membranes. Second, we have begun the process 

of establishing computational strategies for solving 

these mathematical models to enable predictions for the 

thermal and chemical environment inside a biological 

cell. Third, we have started to develop optimization and 

control techniques for investigations of cooling strategies that can be used to help improve 

existing cryoprotocols and to establish new ones.

Anthony Kearsley

Cryopreservation is the maintenance of the viability of 

biological cells, tissues, and organs at very low, cryogenic, temperatures (< −150o C). Cryopreservation, and 

more generally cryobiology—the study of biological organisms at cryogenic temperatures—broadly impacts 

the field of medicine, plays a crucial role in agriculture 

and is important in the fight to maintain earth’s biodiversity. 

Since the first successful cryopreservation of human 

spermatozoa (1954) and later embryos and oocytes (mid 

1980s) cryopreservation has played an increasing role in 

the medical industry for assisted reproduction and in 

vitro fertilization (IVF) [2]. The cryopreservation of 

larger-scale biospecimens (e.g., articular cartilage, the 

cornea, ovarian tissue), which is complicated by their 

larger size, complex shapes and presence of vascular and 

layered structures, is an important capability enabling

organ transplantation and other medical applications, including “biobanking” and “personalized medicine.”

 

13 The Pan-Smithsonian Cryo-Initiative

The agriculture industry relies on cryopreservation 

of embryos and spermatozoa for assisted reproduction,

and to address concerns about preserving farm animal 

genetic diversity. In addition to livestock, biobanking 

has been important for other species as well. A cryobanking initiative based at the Smithsonian Institution13

containing over 1 million samples from over 18,000 species aims to preserve a wide range of biological 

specimens including ones for rare and endangered species. There are also efforts towards preservation of 

genetic materials for agriculture (e.g., seed banks), 

worldwide efforts for cryopreservation of threatened or 

Figure 9. Oocyte or immature ovum.

Figure 10. Discretization of oocyte, a spherical cell at center: RC, 

an aqueous ternary solution between RC and RI and cooling at RO.
22 NIST Applied and Computational Mathematics Division

endangered plant species, as well as other efforts driven 

by the food industry.

There is also considerable interest in the understanding, preservation and processing of frozen 

biological samples in forensic science. For instance, processing at cryogenic temperatures has found a range of 

uses ranging from the detection of volatile substances in 

arson investigations to the recovery of DNA. Other coldtemperature forensic applications, which are in some 

cases more relevant at non-cryogenic temperatures, include the measurement of volatile organic compounds in 

bodily fluids, the postmortem analysis of frozen tissue, 

and the need to understand the stability and degradation 

of evidence contained in frozen samples of bodily fluids, 

tissues and bones.

The role of mathematical sciences in cryobiology is 

on the rise. The development of more effective and 

efficient cooling and warming cryoprotocols for a broad 

range of biospecimens require improved mathematical 

models of thermal, chemical and mass transport processes and sophisticated control and optimization 

schemes (see for example [4]). This project is directed 

towards addressing these needs.

Fundamental scientific questions in the field of cryobiology, as well as practical issues in cryopreservation 

protocols, are incredibly complex and span the breadth 

of plant and animal genetic diversity. This diversity creates an immense challenge for the development of 

cryoprotocols. Even though information gained from 

one species may be helpful in the understanding and development of cryoprotocols for a related species or 

sample type, this is not always the case, and in general a 

cryoprotocol developed for one species may not be 

effective for another species. Indeed, successful cryopreservation varies among individuals within a given 

species and varies with age, for example, for a given individual.

The biological details (plant versus animal, seed 

versus shoot/sprout, cell versus tissue) are coupled in 

critical ways to physical processes such as thermal, mass 

and chemical transport. These transport processes are in 

turn coupled to motion of both phase transforming 

boundaries (e.g., freezing or melting solid–liquid interfaces) and flexible, semipermeable biological 

membranes. The physical processes that are shared 

among these diverse systems, and the associated mathematical descriptions, provide a basis for which 

understanding of cryopreservation can be advanced. 

Also shared among these diverse systems is the goal of 

identifiying optimal cooling, warming and preservation 

strategies measured with respect to various objectives 

such as ice nucleation, chemical toxicity (and ultimately 

survival rates) not to mention time and cost. The predictive capabilities of mathematical and computational 

models to aid in the development of effective cryoprotocols for these systems are thus of considerable 

importance.

Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, 

and these models and theories have been readily and repeatedly applied to cryobiology with much success. 

However, there are significant gaps between experimental and theoretical results that suggest missing links 

in models. One source for these potential gaps is that 

cryobiology is at the intersection of several very challenging aspects of transport theory: it couples multicomponent, moving boundary, multiphase solutions that 

interact through a semipermeable elastic membrane with 

multicomponent solutions in a second time-varying domain, during a two-hundred Kelvin temperature change 

with multi-molar concentration gradients and multi-atmosphere pressure changes. 

In order to address these challenges we have been 

developing, from first principles, a theory of coupled 

heat and mass transport in cryobiological systems accounting for these effects. In our work, we fix ideas to 

the geometrically simple case of the cooling and dehydration of a single cell, such as an oocyte (see Figure 9),

whose primary characterization is that its membrane is 

semi-permeable. 

A major component in the current understanding of 

cryobiology that provides the basis for many prevailing 

cryopreservation strategies is the classical “two factor 

hypothesis” [3]. This hypothesis suggests that an optimal cooling rate lies somewhere between two extremes: 

(1) cool too quickly and the cell cannot remove water 

(dehydrate) fast enough to avoid intracellular ice formation that damages or kills the cell, and (2) cool too 

slowly and chemical toxicity due to overexposure of the 

cell to high solute concentrations causes cell injury or 

death. Successful cryopreservation also in general relies 

on the introduction of additional solutes known as cryoprotective agents (CPAs) into the surrounding fluid. Of 

interest here are membrane-permeable CPAs (e.g., glycerol, ethylene glycol and other small-molecule polyols) 

that enter the cell (and water exits the cell) and have the 

effect of (1) achieving more safely (ideally, at least) a 

desired level of dehydration with a lower intracellular 

salt concentration, and (2) promoting intracellular glass 

formation (vitrification) via an increase in intracellular 

viscosity and decrease in melting temperature while reducing the tendency towards ice formation. Extracellular (non-permeating) CPAs (e.g., glucose, sucrose 

and other sugars) are also used to help dehydrate the cell 

prior to cooling and to promote vitrification.

Our first step in the development of a mathematical 

model for thermal transport, chemical transport, mass 

transport and solidification processes of an externallycooled ternary mixture that surrounds a biological cell, 

was to establish a thermodynamic framework suitable 

for cryobiological applications [1]. This work involved 

the identification of various forms for the Gibbs free energy for non-dilute chemical systems and forms for 

chemical potential gradients used in the definition of 
Summary of Activities for Fiscal Year 2014 23

chemical fluxes. These forms for chemical fluxes involve transport models for both naturally occurring

solutes and the CPAs in these biological systems. Literature on models, experiments and measurements in 

cryobioloigical systems involve a variety of measures of 

chemical composition (e.g., mole fraction, molarity, molality, etc.) and our contributions include formulations 

with respect to these different choices.

Ongoing and future efforts in this direction include 

 the development of bulk transport models as well as 

their coupling to both phase-change (solidification) 

boundaries and the semi-permeable cell membrane, 

 the formulation and computations of partial 

differential equations and coupled boundary conditions specific for a spherical cell geometry 

surrounded by a ternary solution, and

 addressing the cryobiology-driven question of control of the thermal and chemical state of the cell by 

manipulation of the external container temperature.

References

[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] L. Herrero, M. Martínez and J. A. Garcia-Velasco. Current Status of Human Oocyte and Embryo 

Cryopreservation, Current Opinion in Obstetrics and Gynecology 23:4 (2011), 245-250.

[3] P. Mazur, S. Leibo and E. Chu, A Two-factor Hypothesis 

of Freezing Injury: Evidence from Chinese Hamster Tissue-Culture Cells, Experimental Cell Research 71:2

(1972), 345–55.

[4] J. D. Benson, A. J. Kearsley and A. Z. Higgins, Mathematical Optimization of Procedures for Cryoprotectant 

Equilibration using a Toxicity Cost Function, Cryobiology 64 (2012), 144-151.

Participants

Anthony Kearsley, Daniel Anderson, Andrew Dienstfrey 

and Geoffrey McFadden (ACMD), James Benson 

(Northern Illinois University), Adam Higgins (Oregon 

State University)
24 NIST Applied and Computational Mathematics Division

Modeling of Kinetic-based Micro Energy-Harvesters for 

Wearable and Implantable Sensors

The promise of wearable and implantable wireless sensors have generated a great deal of interest in the field 

of health information technology. However, there are 

still numerous challenging issues, including reliability, 

cost, sensing and actuator technology, privacy and security, and power efficiency. RF-enabled wearable 

sensors offer an attractive set of e-health applications,

among which are monitoring of temperature, respiration, heart rate, and blood pressure. As these sensors 

are small and mainly rely on very small batteries to 

carry out their functions, prolonging their operational 

lifetime could significantly help their commercial applications. We are investigating the feasibility of capturing 

and storing kinetic energy from human body motion to 

power such devices. To do this we have developed a statistical model of acceleration generated as a result of 

typical human motion, modeled a micro-harvester device suitable for wearable/implantable applications, 

and modeled and characterized the instantaneous power 

that can be generated by the device. 

Kamran Sayrafian

Energy Harvesting (EH) refers to the process of capturing and storing energy from external sources or ambient 

environment. There are few sources from which we can 

harvest energy for wearable and implantable medical 

sensors, amongst them are body heat and body movement. For example, a thermopile device can be attached 

to the body to convert its thermal energy into electrical 

energy. This is called thermoelectric EH. On the other 

hand, random motion of our arms and legs can generate 

kinetic energy that piezoelectric materials can convert to 

electrical energy. Kinetic energy harvested from human 

body motion seems to be one of the most convenient and 

attractive solutions for wearable or implantable wireless 

sensors in healthcare applications. Due to their small 

size, such sensors have a very limited battery power supply which necessitates frequent recharge or even sensor 

replacement. Energy harvesting can prolong the battery 

lifetime of these sensors. This could directly impact their 

everyday use and significantly help commercial applications such as monitoring of physiological signs (i.e.,

telemedicine).

Kinetic-based energy harvesting devices operate

similarly to a spring and damper system. The direction 

of the force that acts on the mass distinguishes two categories of kinetic-based EH, namely direct versus 

inertial force. With direct force the direction of the force 

opposes the motion; while in the inertial method (i.e.,

acceleration) force is applied along with the motion. The 

most common examples of direct force EH are the heel 

strike, shoe sole (bending the ball of the foot), and knee 

joints (i.e., movement of adjacent body parts). A good 

example of inertial EH that is already in widespread use 

is the kinetic watch. An advantage of inertial EH devices

is that they employ a single attachment point to its internal moving structure; therefore, its overall physical size 

can be minimized as compared to direct force energy 

harvesters. This makes them an appropriate candidate 

for wearable or implantable body sensors that are desired to be very small in size. 

Current research on energy harvesting mostly focuses on device technology. However, a fundamental 

question that needs to be addressed is the amount of harvestable energy which can be made available to

wearable and implantable sensors. Our research objective is to investigate this question by statistical modeling 

of acceleration generated as a result of typical human

motion, modeling of a micro-harvester device suitable 

for wearable/implantable applications, and then modeling and characterizing the instantaneous power that can 

be generated by the device.

To characterize the input acceleration, we have chosen human arm and leg motion, though we plan to 

extend this to other parts of the body as well. At this 

point, the placement of the micro-harvester on the body 

is not the main focus of our research. Instead, we would 

like to have a better understanding of the amount of harvestable energy. To measure acceleration, we use a 

triaxial accelerometer that can be attached to the forearm 

or leg, and secured with a strap to prevent unnecessary 

movement (see Figure 11b).

The measurement samples are time-stamped and 

stored in the on-board memory so that they can be retrieved at a later time. The amplitude and frequency of 

human body acceleration during normal daily activities

can range from -12 g to 12 g and up to 20 Hz respectively. However, there are rare occurrences of higher 

(a) (b)

Figure 11. (a) Histogram of average acceleration of the human 

arm, (b) Placement of the accelerometer.
Summary of Activities for Fiscal Year 2014 25

frequencies, for example at the foot and during heel 

strike when walking. We chose a sampling rate of 64 Hz 

for acceleration measurements with an amplitude range 

of ±6 g. The accelerometer was worn for up to 8 h by 30 

individuals14; a total of 240 h of data were obtained. Participants in this study were staff in NIST’s ITL. Figure 

11a shows the histogram of average acceleration due to 

typical human forearm movement during the day.

Using a mathematical model of an appropriate micro-harvester architecture, namely a Coulomb-force 

parametric generator (CFPG), we developed a methodology [1, 2] to estimate the average generated 

mechanical power from typical human motion. Our preliminary results show that for a small inertial-based 

micro-harvester with dimension 1 cm × 1 cm × 1 mm, 

the average harvested power is around 1 μW to 2 μW

for the forearm and around 4 μW to 10 μW for leg motion. Since wearable/implantable medical sensors are 

envisioned to operate at microwatt levels, such EH 

mechanism seems to be a promising technique for prolonging operational lifetime or equivalently reducing the

required frequency of recharge. 

Next, we have started to model the internal architecture of the CFPG in order to study the temporal 

behavior of the generated power. Having such a dynamic model not only helps to have a more accurate 

estimation of the amount of power generated from various human movements, but also allows us to optimize 

the design or operational parameters of the micro-harvester (e.g., size/dimension, electrostatic holding force, 

etc.) with the characteristics of the input acceleration. To 

achieve this, we used Simulink to create an implementation of the main mechanical component in a CFPG 

device, ensuring that it satisfies all physical constraints 

that impact the generated power. In doing so, we modified the mathematical model (i.e., a nonlinear 

differential equation) that represents the operation of the 

device. The Simulink implementation of this model is 

depicted in Figure 12. Several test scenarios were generated to verify its validity. This model can be used to 

measure the amount of mechanical power generated. 

 

14 Approval for use of human subjects in the course of this study has 

been documented in NIST IRB Case 358.

The conversion to electrical power is done through a

transducer module inside a micro-harvester. We plan to 

develop a Simulink model for the transducer, and study 

the power generated by various input excitations.

Another objective in our study is to characterize the 

impact of the internal micro-harvester physical parameters (e.g., electrostatic force) on the amount of generated 

power. Once set, such parameters are typically kept constant irrespective of the input acceleration. In our 

research, we would like to show that by judiciously 

choosing parameters one can maximize the average generated power. We have formulated and solved an

optimization problem that captures the above statement. 

Preliminary results show that about a 5-fold gain in the 

amount of harvested power can be expected.

Integration of micro-energy harvesting technology 

with wearable sensors seems to be a promising approach 

in prolonging the operational lifetime of wearable and

implantable medical sensors. Optimizing the architectural and design parameters of the harvester device 

based on the characteristics of the input acceleration will 

further increase the amount of the generated power. This 

is a prime example of a cyber-physical system (CPS) 

that highlights how joint design of the cyber and physical components can improve the system efficiency. By 

adaptively tuning the internal parameters of the EH device for various human body motions, one can expect an 

improved efficiency in harvesting kinetic energy. We 

plan to continue this research and study the impact of 

adaptive optimization on the harvestable power using a 

CFPG architecture.

References

[1] N. Yarkony, K. Sayrafian and A. Possolo, Statistical 

Modeling of Harvestable Kinetic Energy for Wearable 

Medical Sensors, in Proc. of the IEEE International Symposium on a World of Wireless Mobile and Multimedia 

Networks, Montreal, Canada, June 14-17, 2010

[2] N. Yarkony, K. Sayrafian and A. Possolo, Energy Harvesting from the Human Leg Motion, in Proc. of the 8th 

Int. Conference on Pervasive Computing Technologies 

for Healthcare, Oldenburg, Germany, May 2014

[3] M. Dadfarnia, K. Sayrafian, P. Mitcheson and J. Baras, 

Maximizing Output Power of a CFPG Micro EnergyHarvester for Wearable Medical Sensors, in Proc. of the 

4th Int. Conference on Wireless Mobile Communication 

and Healthcare, Athens, Greece, Nov. 2014

Participants

Kamran Sayrafian (ACMD), Mehdi Dadfarnia (NIST 

EL), Antonio Possolo (NIST ITL), Paul Mitcheson (Imperial College, UK)

Figure 12. Simulink model of the CFPG main component.
26 NIST Applied and Computational Mathematics Division

Recovery of Background Structures in Nanoscale Helium Ion 

Microscope Imaging

Successful nanoelectronics manufacturing requires high 

quality imaging and accurate measurements at the subnanometer scale. The Helium Ion Microscope (HIM) is 

an important new imaging and metrology tool that can 

provide the needed accuracy. At a given energy level, 

the wavelength of He ions is much smaller than that of 

electrons at the same energy. As a result, HIM imaging 

can produce up to four times higher resolution than is 

possible with current large sample scanning electron 

microscopes (SEM), along with higher contrast and 

greater depth of field. Moreover, the secondary electrons that carry the sample’s surface detail information 

are generated in higher quantities by He irradiation 

than with electron beams, leading to much greater surface detail in HIM images. Indeed, because the 

secondary electron yield is so large, low probe currents 

on the order of one pico ampere, can be used effectively 

to acquire useful HIM images while minimizing damage 

to the sample. These and other advantages of HIM imaging are more fully explored in [10] and [11]. 

However, such low probe currents can induce degradations: HIM images are often noisy, and important 

background structures may not be easily discernible due 

to the weak signal. Techniques that can overcome such 

degradations are of paramount interest. We have discovered an unexpectedly effective recovery and 

enhancement method, which is discussed below. 

Alfred S. Carasso

The first commercial HIM instrument, a Zeiss Orion 

Plus was installed at NIST in 2008, under a cooperative 

research and development agreement. Considerable 

HIM imaging experience has since been accumulated at 

NIST, and that experience is being shared with the manufacturer. One particularly important imaging technique 

developed by the NIST Semiconductor and Dimensional 

Metrology Division, is the fast scan method which produces much sharper images, [4-6]. This methodology 

is based on super-fast acquisition of a large number of 

image frames. Due to the small beam currents generally 

used in scanning particle beam microscopy, these individual frames are inherently very noisy, but exhibit 

significantly less drift-related distortions. The drift correction takes place after finding the center of each frame, 

properly aligning these frames, and adding them together into a single image. Such composed images 

contain much less noise and exhibit significantly less 

blur and deformation than do images obtained by traditional slow scan methods, or images obtained by simply 

adding together fast image frames without compensating for drift. To improve repeatability, this technique 

must be used with the minimum number of fast images, 

which limits the achievable signal to noise ratio. In 

many cases, the resulting composed image is still somewhat noisy and some type of noise processing may be 

beneficial.

Separately and independently, and over several 

years, considerable expertise has been acquired in 

ACMD on the use of Lévy fractional diffusion in image 

restoration, with application to medical and astronomical images [1, 2]. Most recently, [3], a significant new 

application was made to forensic latent fingerprint enhancement. The experience gained in the above 

fingerprint work led to the development of a useful Interactive Data Language (IDL) software routine [8] for 

enhancing noisy HIM images, as well as other images 

in which background structures are not easily discernible due to a weak signal. 

This two stage enhancement approach involves a 

preliminary image-specific adaptive histogram equalization of the given HIM image [12]. Such equalization 

enhances background information while significantly 

magnifying noise, and is not generally advisable with 

noisy data. However, at the second stage, an effective 

and easy to use denoising technique, based on progressive low exponent Lévy fractional diffusion smoothing, 

can be successfully applied to this histogram equalized 

image with magnified noise. As may be inferred from 

Figure 14, such slow motion Lévy smoothing can be 

fine-tuned interactively so as to preserve the detailed

surface morphology of the sample. Comparable fidelity 

to surface detail was not found feasible with some other 

better-known denoising techniques, such as methods

based on minimizing the image “total variation” (TV) 

norm [7, 9], or methods based on thresholding curvelet 

transforms [13, 14]. This is illustrated in Figure 15, 

which should be viewed at high magnification on a high 

resolution monitor. The superior enhancement in Figure 

14 may partially be explained on the basis of Eq. 5.

Progressive Low Exponent Lévy Fractional Diffusion Smoothing. Given a noisy image f(x,y), the 

smoothing procedure results from solving an initial 

value problem for a special type of diffusion equation, 

with the image f(x,y) as initial data. Such smoothing is 

applied to the whole image, and not just to a selected 

portion of the image. With fixed p with 0 < p ≤ 1, consider the linear fractional diffusion initial value problem 

in L

2

(R

2

), 

wt = −(−∆)

pw, t > 0, w(x, y, 0) = f(x, y) (1)
Summary of Activities for Fiscal Year 2014 27

where ∆ denotes the 2D Laplacian. This reduces to the 

classical heat conduction equation when p = 1. However, our smoothing procedure uses values of p « 1, such 

as p = 0.1, for example. Define the 2D Fourier transform 

of the image f(x,y) by

F{f} = f̂(ξ, η)

≡ ∫ f(x, y)exp{−2πi(ξx + ηy)}

R2 dx dy (2)

Eq. 1 has the unique Fourier domain solution

̂w(ξ, η,t) = exp{−t[(2πξ)

2 +(2πη)2

]

p}f̂(ξ, η),

t > 0 (3)

Figure 13. NIST processing of original 600 nm field of view HIM image of Au-decorated gold on carbon sample. Two step process results in a 

companion image displaying significant background structural detail that is not readily apparent in the original image.

Figure 14. Two stage NIST process involves preliminary adaptive histogram equalization in original HIM image (left). This enhances background information but significantly amplifies noise. Second stage (right) applies versatile fractional diffusion smoothing that can filter out noise 

while preserving delicate morphological details.
28 NIST Applied and Computational Mathematics Division

from which w(x,y,t) can be found by inverse Fourier 

transformation

w(x, y,t) = ∫ exp{2πi(ξx + ηy)}

R2

× exp{−t[(2πξ)

2 +(2πη)2

]

p}f̂(ξ, η) dξ dη (4)

As is evident from Eq. 3, w(x,y,t) becomes increasingly 

smoother as t increases. However, for small p, and over 

a short time interval, the smoothed image may be expected to retain many of the essential features present in 

the initial data f(x,y). This expectation is reflected in the 

following sharp inequality which expresses the rate at 

which ‖∇w(. ,t)‖2 becomes infinite as t ↓ 0. With e =

2.71828..., 

‖∇w(. ,t)‖2 ≤ {2pte}

−

1

2p‖f‖2

, t > 0. (5)

In the case of Gaussian smoothing, corresponding to p =

1, this inequality implies ‖∇w(. ,t)‖2 = O(t

−

1

2) as

t ↓ 0. In contrast, ‖∇w(. ,t)‖2 = O(t

−5

), ~as t ↓ 0, 

when p = 0.1. This suggests that for small t > 0 and p « 

1, the solution w(x,y,t) retains considerably more of the 

small scale features in the initial data f(x,y), than is the 

case with Gaussian smoothing. The above inequality 

may also possibly explain why Lévy fractional diffusion 

smoothing in Figure 14 leads to higher fidelity than is 

the case with the methods used in Figure 15.

IDL Code for FFT Implementation of Slow Motion 

Lévy Smoothing. Adaptive histogram equalization is a 

useful enhancement technique for images where significant information is suspected of being hidden in dark 

regions. However, in practice, usefully recovered background information is often obscured by the 

amplification of the accompanying noise, and the resulting improvements may not be particularly helpful 

without additional intervention. Here, the adaptively 

equalized HIM image is used as the initial data f(x,y) in 

Eq. (1). Forward and inverse FFT are used to implement 

the operations in Eq. 3 and Eq. 4 respectively, at any t > 

0. After pre-selecting the Lévy exponent p, and a tentative maximum smoothing time Tmax at which to 

terminate the smoothing process, Eq. 4 can be evaluated 

at finitely many intermediate times 0= t0 < t1 < t2 < t3 < 

... = Tmax, to create a suite of progressively smoother

images. Such a suite can be acquired and displayed in a 

few seconds, even with 1024 × 1024 pixel images. Several different pairs (p, Tmax) can be explored in a matter 

of minutes.

The success of this method in practice derives in 

large measure from the ability to explore efficiently in 

parameter space and visually select the best result. There 

is no single set of parameters that will be useful in all 

cases, nor is there an automatic way of selecting the best 

set of parameters. However, a trained and experienced 

human analyst can generally locate useful parameter 

values and determine the proper amount of fine tuning 

that best displays the information sought.

The example in Figure 16 demonstrates significant 

background recovery and sharpening in a HIM image. 

Useful application of the method to a fast scan composed SEM image, is shown in Figure 17. Note the low 

values of p and t in these images and in Figure 13.

Figure 15. Split Bregman Total Variation (TV) denoising (left) generally does not preserve small-scale surface detail with sufficient fidelity. 

Denoising using Curvelet Thresholding (right) is time-consuming, and can generate misleading artifacts. Here, spurious criss-crossing lines in 

Curvelet image become clearly visible under magnification, when viewed on high resolution monitors.
Summary of Activities for Fiscal Year 2014 29

References

[1] A. S. Carasso, The APEX Method in Image Sharpening 

and the Use of Low Exponent Lévy stable laws, SIAM 

Journal on Applied Mathematics 63 (2002), 593–618.

[2] A. S. Carasso, APEX Blind Deconvolution of Color Hubble Space Telescope Imagery and Other Astronomical 

Data, Optical Engineering 45 (2006), 107004.

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

Fingerprint Enhancements, Journal of Research of the 

NIST 119 (2014).

Figure 16. NIST processing of original 1.5 μm field of view HIM image of Au decorated tin ball sample.

Figure 17. NIST processing of composed SEM image of platinum decorated gold on carbon sample, with a field of view of 441 nm.
30 NIST Applied and Computational Mathematics Division

[4] P. Cizmar, A. E. Vladár and M. T. Postek, Real-time 

Scanning Charged-particle Microscope Image Composition with Correction of Drift, Microscopy and 

Microanalysis 17 (2010), 302-308.

[5] P. Cizmar, A. E. Vladár and M. T. Postek, Advances in 

Modeling of Scanning Charged Particle Microscopy Images, Proceedings of the SPIE 7729 (2010), 7729OZ.

[6] P. Cizmar, A. E. Vladár and M. T. Postek, Advanced Image Composition with Intra-frame Drift Correction, 

Proceedings of the SPIE 8036 (2011), 80360D.

[7] T. Goldstein and S. Osher, The Split Bregman Method for 

L1 regularized problems, SIAM Journal on Imaging Science 2 (2009), 323–343.

15

[8] ITTVIS Interactive Data Language (IDL), http://www.exelisvis.com/IDL.aspx.

[9] A. Marquina and S. Osher, Explicit Algorithms for a New 

Time Dependent Model Based on Level Set Motion for 

Nonlinear Deblurring and Noise Removal, SIAM Journal 

on Scientific Computing 22 (2000), 387–405.

[10] M. T. Postek and A. E. Vladár, Helium Ion Microscopy 

and its Application to Nanotechnology and Nanometrology, Scanning 30 (2008), 457-462.

[11] M. T. Postek, A. Vladár, C. Archie and B. Ming, Review 

of Current Progress in Nanometrology with the Helium 

Ion Microscope, Measurement Science and Technology

22 (2011), 1–14.

[12] W. K. Pratt, Digital Image Processing, (2012), Wiley-Interscience, New York.

[13] R. Sivakumar, Denoising of Computer Tomography Images using Curvelet Transform, ARPN Journal of 

Engineering and Applied Sciences 2 (2007), 21–26.

[14] J. L. Starck, E. J. Candès and D. L. Donoho, The Curvelet 

Transform for Image Denoising, IEEE Transactions on 

Image Processing 11 (2002), 670-684.

Participants

Alfred S. Carasso (ACMD) and Andras Vladár (NIST 

PML)

 

15 See also http://www.math.ucla.edu/ tagoldst/code.html.
Summary of Activities for Fiscal Year 2014 31

High Precision Calculations of Fundamental Properties of FewElectron Atomic Systems 

Atomic structure calculations have always had a large 

impact in spectroscopy. They not only are invaluable in 

the analysis of complex spectra by providing reliable 

term positions and level designations, but they also contribute to an understanding of the underlying physical 

processes. Our work is devoted to the development of a 

rigorous method that delivers energy levels for small 

atomic and molecular systems of such a high precision 

as to enable the prediction, theoretically, of fundamental 

atomic properties more accurately than even the most 

accurate experiments.

James Sims

NIST has long been involved in supplying critically 

evaluated data on atomic and molecular properties such 

as the atomic properties of the elements contained in the 

Periodic Table and the vibrational and electronic energy 

level data for neutral and ionic molecules contained in 

the NIST Chemistry WebBook16. Fundamental to this 

endeavor is the ability to predict, theoretically, a property more accurately than even the most accurate 

experiments. It is our goal to be able to accomplish this 

for few-electron atomic systems. 

The revolutions in physics in the early decades of 

the past century provided essentially exact, predictive 

theories for all chemical properties and processes. However, the mathematical intractability of the Schrödinger 

equation prevented the computation of accurate numerical solutions for either atomic or molecular systems 

until recently. In the past two decades, there have been 

breathtaking improvements in computer hardware and 

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

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

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

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

one-electron functions. Such configuration interaction 

(CI) methods have been quite successful in approaching 

or reaching experimental accuracy for relative energies 

of modestly-sized atoms and molecules. However, orders of magnitude improvements are needed to expand 

the world’s spectroscopic database into currently inaccessible realms, establish its building blocks beyond 

dispute, and supersede more expensive experimental approaches. 

 

16 http://webbook.nist.gov/chemistry/

The essential flaw in theoretical methods built on 

the orbital approximation is their inability to correctly 

describe the mathematical cusp behavior of many-body 

wave functions in regions of close electron proximity, 

the so-called electron cusp region of the exact electronic 

wave function [1-3]. This flaw leads to incomplete accounting of instantaneous, short-range correlation 

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

method to solve the electron cusp problem and bring 

subchemical accuracy to atomic systems with more than 

two electrons. A depiction of the electron-electron cusp 

in an essentially exact Hy-CI wave function of the helium (He) atom ground state is shown in Figure 18. In 

the region of the electron coalescence point, the exact 

wave function is linear in the interelectronic distance 

(r12). However, conventional quantum chemical CI 

wave functions, which effectively incorporate only even 

powers of r12, do not have sufficient flexibility to fully 

relax into the conical region of the cusp, and thus poorly 

account for the short-range electron correlation. In Figure 18, these deficiencies are clearly exhibited by CI 

wave functions using special analytical and numerical 

techniques for extremely high angular momentum (l) 

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

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

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

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

Figure 18. Failure of conventional CI wave functions to describe 

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

Cartesian coordinate space can be envisioned by reflecting the plots 

about the vertical axis.
32 NIST Applied and Computational Mathematics Division

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

accurate to only 5 decimal places, demonstrating that 

converging absolute energies even to the μh level is essentially impossible in practical computations with 

orbital treatments. In contrast, the early work of 

Hylleraas [5] showed the astounding superiority of explicitly-correlated methods, which directly incorporate 

the r12 variable into the wave function. Our hybrid 

Hylleraas-CI result shown in Figure 18 achieved better 

than 20 digits of accuracy in the absolute energy [4], at 

least 14 orders of magnitude better than the best conventional CI treatments, a result that is “essentially exact for

all practical purposes.” The challenge for computational 

scientists is to extend the phenomenal accomplishments 

on atomic helium to three, four, and more electron states 

and to molecular systems.

Hylleraas's original method (Hy) has been extended 

to three electrons [6, 7] resulting in some of the most 

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

to date, way beyond spectroscopic accuracy. Like helium, virtual experiments can be done that are more 

accurate than current experimental capabilities, but not 

without huge computational costs. (The lithium calculations require an estimated 6,000 times more 

computational power than helium). However, already at 

the four electron level there are significant unresolved 

integration problems with the original Hy approach. 

The central problem, from a computational point of 

view, is how to represent the electron-electron correlations without the mathematical and computational 

problems becoming prohibitive. To get around this 

problem and make calculations of spectroscopic accuracy or better for systems with more than three electrons, 

we have developed a hybrid Hy-CI method that merges 

the ease of calculation of the CI method with the more 

rapid convergence of the Hy method in such a way that 

it offers the hope of breaking the four electron integral

barrier. (With only a single rij in any term, the most difficult integrals are the four electron integrals which are 

present in beryllium.) This would enable extension to 

systems with more than four electrons. 

We are exploring the utility of our hybrid Hy-CI 

method for both three electron lithium systems and the 

four electron beryllium atom and its iso-electronic sequence. In the case of lithium, we have computed four 

excited states of the lithium atom to two orders of magnitude greater than has been done before [8]. In the case 

of beryllium, not only has the ground state non-relativistic energy of the atom been calculated, but also the 

same property has been calculated for the entire beryllium iso-electronic sequence, i.e., all four-electron ions 

of all the elements in beryllium's column in the periodic 

table, to historic levels of accuracy, in some cases reducing the error by a factor of a thousand or more. Figure 

19 shows the result, where the smooth nature of the 

curve that results from the data points is evident.

The importance of the current results is that accurate and dependable compilations of non-relativistic 

atomic energies are useful calibration points for the development of more sophisticated models used in 

electronic structure calculations. In addition, the calculation of physical energies of interest, e.g., a transition 

energy or familiar chemical ionization potentials or electron affinities, involve these non-relativistic energies. So 

the non-relativistic energies need to be calculated accurately to guarantee the accuracy of the result, and hence

can be regarded as fundamental atomic data. Once they 

have been computed “essentially exactly for all practical 

purposes,” as in the current case, they can be used to obtain more and more accurate ionization potentials, 

electron affinities, etc., as the other (correction) terms 

become known to increasing accuracy. 

The results of the beryllium iso-electronic sequence 

study were published recently in the Journal of Chemical Physics [9]. All results reported in the paper were 

obtained using quadruple precision (30+ digits) floating 

point subroutines written in Fortran 90 and utilize parallel computing. For a 79,137-term wave function we 

achieved a factor of 120 speedup on 128 processors for 

the O(n

3

) step running on NIST's cluster of 7892 Intel/AMD 64-bit processors running CentOS Linux. The 

availability of the Z expansion given in our article opens 

up access to interesting applications such as the critical 

charge below which the four electron atom is not bound.

In the coming year we plan to continue to develop 

the four electron integral mathematics and codes, including the publication of a paper on fast, efficient, and 

accurate calculations of four electron integrals. The improved codes will be used in a benchmark calculation on

the Be atom as well as eventually in a calculation on an 

N > 4 electron system.

Figure 19. Plot of non-relativistic energies in hartrees versus nuclear charge Z for Z = 4 through 113.
Summary of Activities for Fiscal Year 2014 33

References

[1] T. Kato, On the Eigenfunctions of Many-particle Systems 

in Quantum Mechanics, Communications in Pure and 

Applied Mathematics 10 (1957), 151-177.

[2] R. T. Pack and W. B. Brown, Cusp Conditions for Molecular Wavefunctions, Journal of Chemical Physics 45

(1966), 556-559.

[3] W. Kutzelnigg and J. D. Morgan III, Rates of Convergence of the Partial-wave Expansions of Atomic 

Correlation Energies, Journal of Chemical Physics 96

(1992), 4484-4508.

[4] J. S. Sims and S.A. Hagstrom, High precision Hy-CI Variational Calculations for the Ground State of Neutral 

Helium and Heliumlike Ions, International Journal of

Quantum Chemistry 90 , 1600-1609 (2002).

[5] E. A. Hylleraas, Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von 

Ortho-Helium, Zeitschrift für Physik 54 (1929), 347-366.

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

Precision Atomic Theory for Li and Be+: QED Shifts and 

Isotope Shifts, Physical Review Letters 100 (2008), 

243002.

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

of Li and Be+ using Explicitly Correlated Functions,

Physical Review A 80 (2009), 020101.

[8] J. S. Sims and S. A. Hagstrom, Hy-CI Study of the 2 Doublet S Ground State of Neutral Lithium and the First Five 

Excited Doublet S States, Physical Review A, 80, 2009.

[9] J. S. Sims and S. A. Hagstrom, High Precision Calculation of the Nonrelativistic Energies for the Ground States 

of the Beryllium Isoelectronic Sequence Up Through Z = 

113, Journal of Chemical Physics 140 (2014), 224312.

Participants

James Sims (ACMD) and Stanley Hagstrom (Indiana 

University)
34 NIST Applied and Computational Mathematics Division

Rheology of Dense Suspensions

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

such as suspensions, is of importance in many industries 

such as pharmaceuticals, coatings, and concrete. These 

fluids are disordered systems consisting of a variety of 

components with disparate properties that interact in 

many different ways. Modeling and predicting the flow 

of such systems represents a scientific challenge requiring large scale computer simulations. In collaboration 

with scientists in NIST’s Engineering Laboratory, we 

are developing a software system capable of performing 

large scale simulations of dense suspensions. It is highly 

parallel and has been shown to efficiently scale up to at 

least 128,000 processors on a DOE supercomputer. Our 

main goal is to advance understanding of the flow properties of a specific material, fresh concrete, a dense 

suspension composed of cement, water, sand, and rocks.

Our current focus is on enabling the use of vane 

rheometers for measuring the flow properties of fresh 

concrete, something not currently possible. While existing “concrete rheometer” measurements can be found 

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

will result in complex local stress and strain/strain rate 

fields. Our simulations will enable us to map out these 

fields, in 3D, and bring insight into the vane design process, leading to optimized vanes for both measurement 

and mixing applications. 

We are also using this simulator to help design new 

standard reference materials (SRMs) which will be used 

for calibrating mortar and concrete rheometers. Results 

from the simulation of a recently released cement SRM 

(SRM 2492) [1] are being used in in the development of 

SRMs for both mortar and concrete, which are expected 

to be released within the next few years. These SRMs 

will use uniform size hard spheres as the suspended particles. An early test simulation is shown in Figure 20.

William George

Concrete is the most widely used building material in 

the world, representing a 100 billion dollar industry in 

the US upon which our nation’s physical infrastructure 

relies. There is now a strong interest in making concrete 

a more sustainable material by finding new ways to recycle it, and by changing its ingredients in order to 

reduce the amount of green-house gas from its production. (According to the World Business Council for 

Sustainable Development, the manufacture of concrete’s key ingredient, cement, is responsible for at least 

5 % of global carbon dioxide production.) As new mixture designs for concrete are developed to meet these 

needs, it is important to measure and control rheological 

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

specifications. Failure to control the flow of concrete on 

a job site can lead to significant cost overruns and delay.

Fluids are characterized by yield stress and viscosity, properties which can vary as a function of shear rate. 

Yield stress is the force applied per unit area to initiate 

a flow. Viscosity is the applied force per unit area 

needed to maintain a shear rate. Shear rate is the velocity 

gradient perpendicular to the flow direction. The local 

stress in a vane rheometer is illustrated in Figure 21.

Many factors control viscosity and yield stress. For 

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

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

their shape and size distribution. There can be great variations in materials depending on their history and where 

they were obtained. For example, rocks from quarries 

are usually angular because they are crushed when processed, whereas rocks obtained from river beds are 

typically rounded due to erosion. Additionally, it turns 

out that the more similar in size the rocks in a concrete 

suspension, the harder it is to get that concrete to flow. 

In this case, the concrete may actually jam when poured 

through a narrow opening, causing construction delays. 

Clearly, to optimize the flow properties of concrete and 

other suspensions, one needs to understand the relationship between flow and properties of the fluid’s 

constituents.

Figure 20. Snapshot of a 6-blade vane rheometer simulation. The 

suspended spheres are color coded by the section in which they 

started. Only 6 of the 12 sections are shown here in order to see 

details around the vane blades.
Summary of Activities for Fiscal Year 2014 35

QDPD. Our application, QDPD (Quaternion based Dissipative Particle Dynamics) [2], uses two computational 

methods for simulating fluid flow: Dissipative Particle 

Dynamics (DPD) [3] and Smoothed Particle Hydrodynamics (SPH) [4]. These are both mesh-free Lagrangian 

methods in which the fluid is represented as a set of 

mesoscopic particles that move in a continuous space, 

with each particle accounting for the microscopic particles in a small volume of fluid. Forces between these 

particles are limited in range allowing for a highly parallel implementation of these methods. This is similar to 

traditional molecular dynamics (MD) in that particles 

move according to Newton's laws, however the interparticle interactions are designed such that much larger 

time-steps can be used in the algorithm when compared 

to MD simulations. This allows for the study of physical 

behavior that occurs on time scales many orders of magnitude larger than what would be possible using MD 

techniques. Each solid object (e.g., a rock, or grain of 

sand) in a simulation is represented by a group of these 

DPD/SPH particles that are further constrained to always move such that their positions relative to the other 

particles that comprise the solid object remain unchanged.

In addition to the forces computed using the DPD 

and SPH techniques, other forces are computed to better 

account for the interaction between the suspended particles, that is, the sand and gravel. These additional forces 

include lubrication forces that help keep the particles 

separated, and, to model colloidal systems, van der 

Waals forces that introduce an attractive interparticle interaction and Brownian forces are utilized.

The original DPD algorithm used an Euler method

for updating the positions of the free particles, that is, 

the particles that represent the fluid, and a leap-frog algorithm for updating the positions of the solid objects. 

The NIST algorithm, called QDPD, is a modification 

that uses a velocity Verlet method to update the positions of both the free particles and the solid objects. In 

addition, the solid object motion is determined from the 

quaternion-based scheme of Omelyan [5] (hence the Q 

in QDPD). 

A typical simulation may entail keeping track of up 

to 100,000 solids of varying shape and size. Further, 

many of the forces between particles depend on the local 

surface curvature of the aggregate at points close to 

neighboring aggregates, which requires keeping track of 

the location, orientation and shortest distance between 

neighboring solids. Clearly, modeling such systems necessitates large scale simulations to accurately predict 

their properties. We have adopted and developed some 

novel approaches, originally based on cellular automata 

methods that can successfully take into account many of 

the features of a suspension. QDPD has been validated 

by both theory and experiments on idealized systems 

and has been extended to account for random shaped objects with different interparticle interactions.

Starting with the original serial version of this simulator we enhanced QDPD to utilize the power of large 

parallel machines regularly using 8000+ processors, 

and, for large production runs, using up to 128,000 processors when running on the IBM Blue Gene/Q, Mira, 

at the Leadership Computing Facility of Argonne National Laboratory. QDPD remains under constant 

development to improve its capabilities as well as to improve its parallel performance. 

Supercomputer Access. During the 2014 calendar year 

we have had access to the IBM Blue Gene/Q supercomputer Mira, having been awarded 40 million CPU-hours 

of compute time on this machine from the DOE INCITE 

program (Innovative and Novel Computational Impact 

on Theory and Experiment). This access has enabled us 

to perform several very large simulations of 4-blade and 

6-blade vane rheometers. 

Visualization. A major part of this project involves the 

development and use of specialized visualization software to investigate the results of our simulations. This 

includes both the display of the systems under study as 

well as techniques to probe and measure aspects of the 

system we are viewing. For performance reasons we rely 

heavily on the programmable capabilities of GPUs 

(Graphics Processing Units). For example, within the 

images in each of the figures, each suspended sphere is 

rendered within the GPU as a point sprite, i.e., a 2D textured image at a single 3D point, which requires only 

Figure 21. A snapshot of a 4-blade vane rheometer simulation displayed with a volume visualization of the magnitude of the local 

stress within the system. As in Figure 20, the suspended spheres are 

color coded by the section in which they started. Only 4 of the 8 

sections are shown here in order to see details around the vane 

blades. For the added volume visualization, stress is color-coded 

from yellow (low stress), to green (high stress), with stresses below 

a set threshold show in light purple.
36 NIST Applied and Computational Mathematics Division

location and size information for display, rather than using a polygonal representation of these spheres. We also 

use volume visualization techniques to display various 

properties within the system, such as in Figure 21 which 

shows the local stress value throughout the system. As 

shown in Figure 22 and Figure 23, we can interactively 

probe a system to compute and show values of properties at specific locations or areas in the system. All of 

our visualizations can also be used within our 3D immersive visualization system for full immersion into the 

simulated systems. This display system consists of three

large displays (each approximately 2.5 m by 2.5 m), arranged as two walls and a floor forming the corner of a 

cube.

Results. Over the last few years our simulations have 

provided fundamental insights into mechanisms that 

control the onset of flow in suspensions that can be 

linked to macroscopic properties such as yield stress and 

viscosity. We have developed a novel way of describing 

the interparticle stress fields and their spatial correlations and through this technique it was discovered that 

under shearing, although the suspended particles remain 

in a liquid order, the interparticle stress is strongly anisotropic [6, 7]. In addition, a transition under flow was 

observed: during a transient regime at low deformation, 

the stress propagates along the compression direction of 

the shear, whereas at larger deformations the stress is organized into layers parallel to the flow direction. 

Further, we found that yield stress is shear rate dependent [8]. The higher the shear rate the greater the yield 

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

stress was found to go to zero as a consequence of temperature effects. Further, by examining the very long 

time scale behavior of the rocks, we can link their motion to viscoelastic properties of the suspension.

We have recently modeled cementitious materials 

composed of cement and fly ash [9]. Here we studied 

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

angular shaped particles (cement) combined with 

smaller spheres (representing ultra fine fly ash), and 

found that there is a decrease in yield stress and viscosity 

of the suspension in comparison with the same system 

without fly ash.

From our studies, we have discovered that, given 

the rheological properties of a non-Newtonian fluid matrix we can predict the rheological properties of 

suspensions composed of hard spheres in the fluid [10]. 

We are applying these ideas to predict the flow of dense 

suspensions consisting of 1 mm diameter glass beads 

suspended in a matrix fluid of known properties, NIST 

SRM 2492 [1]. Such suspensions are currently being 

evaluated as a new candidate SRM for mortars. As a 

consequence of this discovery, one only needs to measure the fluid properties of the matrix fluid, which is 

generally far easier to do than measuring the suspension

itself. Hence, fewer experiments are needed to obtain the 

rheological properties, thus saving cost and time. Currently these results apply only to hard sphere 

suspensions, however. In the coming year we plan to test 

this scaling approach on suspensions composed of more 

complex shaped inclusions.

Potential Impact. Our results can be used to accelerate 

the design of new high-performance cement-based materials by reducing the time and costs associated with 

research and development. For example, the ability to 

use computational models to study suspensions would 

Figure 22. Interactively positioning a line probe in a system. Each 

endpoint is indicated with a 3D cursor consisting of 3 orthogonal 

pairs of small cones surrounding the chosen point. The endpoints 

of this line probe can be positioned anywhere within the simulation 

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

of the stress have been turned off for this image in order to highlight 

the probe.

Figure 23. This is the identical display as in Figure 4 except that 

now we have turned on the volume visualization of the stress data 

as well as some of the hard spheres. The stress along the probe line 

is shown in the sub-window labeled “Stress Profile.” This plot is 

dynamically generated and updates each frame as the simulation is 

animated.
Summary of Activities for Fiscal Year 2014 37

accelerate research into waste stream processing, in 

which industrial waste materials are incorporated into 

cement with the goal of maintaining or enhancing concrete performance, while at the same time reducing the 

environmental impact of this industrial waste. One such 

candidate waste material is fly ash, which has been 

shown to be useful as a substitute for some portion of 

the cement used in concrete. Reducing the need for cement would lead to a reduction in the production of 

carbon dioxide related to cement production.

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

based materials such as concrete, an improved general 

understanding of rheological properties derived from 

this research should have a broad impact. Suspensions 

are utilized in a wide variety of technological processes 

and, as our study is largely parametric in nature, results 

will be transferable to other suspensions of interest such 

as nanoparticle systems. Understanding mechanisms for 

the dispersion or agglomeration of such systems remains 

a challenge in many industries ranging from pharmaceuticals to coatings.

References

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

Guthrie, Certification of SRM 2492: Bingham Paste Mixture for Rheological Measurements, NIST Special 

Publication SP 260-174 Rev. 2012.

[2] N. Martys, Study of a Dissipative Particle Dynamics 

Based Approach for Modeling Suspensions, Journal of

Rheology 49:2 (2005), 401-424.

[3] P. J. Hoogerbrugge and J. M. V. A. Koelman, Simulating 

Microscopic Hydrodynamic Phenomena with Dissipative 

Particle Dynamics, Europhysics Letters 19 (1992), 155-

160.

[4] J. J. Monaghan, Smoothed Particle Hydrodynamics, Reports on Progress in Physics 68 (2005), 1703–1759.

[5] I. P. Omelyan, On the Numerical Integration of Motion 

for Rigid Polyatomics: the Modified Quaternion Approach, Computer Physics 12 (1998), 97.

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

Contact and Stress Anisotrophies in Start-up Flow of Colloidal Suspensions, Physical Review E 80 (2009), 

031401.

[7] P. Hebraud, D. Lootens, and N. Martys. “Stress Organization in an Attractive Concentrated Colloidal 

Suspension under Flow,” XVIth International Conference 

on Rheology, Lisbon, Portugal, August 5, 2012.

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

Hebraud, Stress Propagation in a Concentrated Colloidal 

Suspension under Shear, European Physics Journal E 35

(2012), 20.

[9] N. S. Martys, Multiscale Modeling of the Flow of Cement 

Based Materials, in Rilem State of the Art Report on Numerical Simulations of Fresh Concrete Flow, August 

2010.

[10] 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.

Participants

William George, Steven Satterfield, Marc Olano, and 

Judith Terrill (ACMD), Nicos Martys and Clarissa Ferraris (NIST EL), Edward Garboczi (NIST MML), Pascal 

Hébraud (CNRD/ESPCI, France)
38 NIST Applied and Computational Mathematics Division

DLMF Standard Reference Tables on Demand

Mathematical software designers, numerical analysts 

and other researchers often need high quality tables of 

function values, but most current libraries and systems 

that produce such tables offer limited information about 

accuracy. To address this void, NIST ACMD and the 

University of Antwerp Computational Mathematics 

(CMA) Research Group are collaborating to build the 

DLMF Standard Reference Tables (DLMF Tables) web 

service. DLMF Tables will provide a standard of comparison for testing numerical software by computing, on 

demand, special functions to user-defined accuracy with 

guaranteed error bounds. ACMD is building and integrating the site’s front end user interface with CMA’s 

back end computational engine based on their MpIeee 

library, an IEEE compliant C++ library for base 2

n or 

10m mixed precision floating point arithmetic. We recently released a beta version, marking the completion 

of the first phase of the web service development project. 

More functions are in the pipeline, and additional site 

enhancements and comprehensive testing are currently 

in provess.

Bonita Saunders

Numerical software designers and application programmers typically use tables of elementary and special 

functions in order to test software or validate numerical 

computations. Although searching through published 

tables was once the norm, this has been superseded by 

the use of specialized software libraries, computer algebra systems, or online computing facilities. 

Unfortunately, most results obtained with these tools 

come with little information about the accuracy of the 

results. One notable exception is MpIeee [2-5], a C++ 

multiple-precision floating-point library developed and 

maintained by the University of Antwerp Computational 

Mathematics (CMA) Research Group. MpIeee, which

covers a substantial subset of special functions, uses algorithms based on series and continued fraction 

representations, in conjunction with a detailed analysis 

of the rounding errors that allows results to be computed 

to 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. 

The high quality of the CMA Research Group’s

work in the field of software for special functions over 

many years has driven ACMD’s decision to collaborate 

with CMA to build the DLMF Standard Reference Tables (DLMF Tables) web service17, an online service 

 

17 http://dlmftables.uantwerpen.be/

that allows users to create their own tables of special 

function values with an error certification. ACMD is 

building the front end user interface to work with the 

back end computational engine based on the MpIeee library. 

The top level structure of DLMF Tables is organized according to the NIST Digital Library of 

Mathematical Functions (DLMF). As Figure 24 shows, 

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 25) for that chapter appears; the user chooses a 

function and requests either a tabulation or comparison. 

This determines what additional user input will be required. Users will note that each function description 

contains a link to the definition in the DLMF.

Figure 24. Table of contents for DLMF Tables website.

Figure 25. Input screen for Fresnel integral C(x).
Summary of Activities for Fiscal Year 2014 39

Tabulation. Once a user selects Tabulation he may either enter function parameters and argument data 

directly into the form or upload a data file meeting the 

site’s format specifications. The user may request up to 

500 output digits and choose a mode for computation. 

The default output mode is interval mode, where a strict 

enclosure (lower and upper bound) is displayed for each 

requested function value. For example, if the user requests n digits, the computed function values are 

displayed in scientific notation with n digits, plus five 

extra digits (displayed smaller), along 

with exclusive error bounds (digits 

after ±) as shown in Figure 26. In 

most cases, this allows the user to determine the value to the desired 

number of digits using whatever 

rounding or truncation scheme preferred. No extra digits are shown 

when the computed value is exact.

Alternatively, instead of an interval enclosure the user may explicitly 

choose that output values be displayed exactly in one of the following 

rounding modes:

 round to nearest (even)

 round up (toward +∞)

 round down (toward -∞)

 round toward 0

 round away from 0.

When a rounding mode is chosen, 

output is shown with the number of 

digits requested without extra digits.

Comparison. When the user selects 

Comparison, a user-supplied data file 

is uploaded. The output table displays 

the reference values, computed in one 

of the user selected modes described 

above, 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 27.

In particular, if the user uploads 

a file containing n-digit function values for a comparison based on 

interval mode, the upper and lower 

error bounds associated with each 

reference value form a sharp interval 

enclosure for the reference function 

evaluation. To accommodate possible rounding or truncation used to 

produce the uploaded values, we take 

the floor of the left endpoint (round 

toward -∞) and the ceiling of the right 

endpoint (round toward +∞) to n digits.

If the user’s value falls outside this expanded interval, incorrect digits are highlighted in red and the user 

will see the message Value not in interval enclosure at 

requested precision when the cursor is placed near the 

dagger adjacent to the uploaded number.

If the user’s value falls within the expanded interval 

(endpoints included), but does not match the round to 

nearest (even) value computed from the reference value, 

Figure 26. Output table for Bessel function Jυ

(x).

Figure 27. Output for comparison of DLMF Tables computations with table of function values submitted by user.
40 NIST Applied and Computational Mathematics Division

digits in question are highlighted in yellow and the message will state Value not equal to round to nearest.

If the comparison is based on one of the rounding 

modes, the rounded reference values are exact and differences with the user’s values are highlighted in red 

with the error message Value is not correct.

Launch. To allow a quick launch of the system, the first 

phase, or beta version, is being hosted at the Antwerp 

site. A public announcement of the site was published in 

the SIAM OP-SF newsletter [6] and NA-Digest [7]. 

Other activities included the publication of a proceedings paper based on talks given by Annie Cuyt and 

Daniel Lozier at the Workshop on Numerical Software: 

Design, Analysis, and Verification, Santander, Spain, 

July 4-6, 2012 [1], and a talk and poster on the project 

presented by Daniel Lozier at the Institute for Computational & Experimental Research in Mathematics 

(ICERM) Workshop at Brown University [8]. 

Future Work. Code verification and the trapping of bogus input data are of current concern. Bruce Miller and 

Chris Schanzle have worked on the input data problem, 

but algorithm and code verification is still needed. To 

help with this task, Andrew Dienstfrey is developing a 

formal testing structure where test results are carefully 

documented and stored in a repository. The repository 

will contain all test data files so that results can be duplicated when necessary. 

In addition to testing, our immediate focus includes 

increasing the number of functions offered, inserting 

more user documentation, and possibly adding more extensive documentation for programmers. Once the 

DLMF Tables site is stabilized, we will have to tackle 

deferred decisions about its integration with the DLMF 

and its permanent location. 

References

[1] 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.

[2] M. Colman, A. Cuyt and J. Van Deun, Validated Computation of Certain Hypergeometric Functions. ACM

Transactions on Mathematical Software 38:2 (2012), Article 11.

[3] 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.

[4] A. Cuyt, V. B. Petersen, B. Verdonk, H. Waadeland and 

W. B. Jones, Handbook of Continued Fractions for Special Functions. Springer, New York, 2008.

[5] A. Cuyt, B. Verdonk, H. Waadeland, Efficient and 

Reliable Multiprecision Implementation of Elementary 

and Special Functions, SIAM Journal on Scientific

Computing 28 (2006) 1437-1462.

[6] M. Muldoon and D. Dominici (eds.), OP-SF NET 22:1

(January 2015), SIAM Activity Group on Orthogonal 

Polynomials and Special Functions.

[7] D. Dunlavy (ed.), NA-Digest 15:2 (January 15, 2015).

[8] H. Cohl, D. Lozier, Outgrowths of the Digital Library of 

Mathematical Functions Project, Institute for Computational & Experimental Research in Mathematics 

(ICERM) Workshop on Challenges in 21st Century Experimental Mathematical Computation at Brown 

University, July, 2014.

Participants

Bonita Saunders, Bruce Miller, Marjorie McClain, Daniel Lozier, Andrew Dienstfrey and Chris Schanzle 

(ACMD), Annie Cuyt, Stefan Becuwe, and Franky 

Backeljauw (U. Antwerp)

http://dlmftables.uantwerpen.be/
Summary of Activities for Fiscal Year 2014 41

Part III: Project Summaries

 Part III

Project Summaries
42 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2014 43

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.

Modeling and Optimization in 

Cryobiology

Anthony Kearsley

Daniel Anderson

Andrew Dienstfrey

Geoffrey McFadden

James Benson (Northern Illinois University)

Adam Higgins (Oregon State University)

See page 21.

Recovery of Background Structure 

in Nanoscale Helium Ion Microscope 

Imaging

Alfred S. Carasso

Andras Vladár (NIST PML)

See page 26.

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, supported for the past four 

years by an Innovations in Measurement Science (IMS) 

grant, proposes a revolutionary, table-top x-ray imaging 

system to capture the motion of electrons, atoms, and 

molecules on femtosecond time scales and with picometer spatial resolution.

The combination of table-top x-ray lasers, a dramatic recent breakthrough developed at JILA, with 

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

Electronics and Photonics Division, promises to enable 

these new measurement capabilities. The integration of 

these components, accompanied by significant increase 

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

extraordinary TES energy resolution, requires new data 

modeling and processing techniques. These techniques 

will overcome current limitations by

 Resolving temporal overlap in photon detection 

while achieving energy resolution of temporally 

isolated arrivals,

 Improving efficiency in elimination of 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 are being developed and 

characterized that rely on this knowledge but are suitable for overlapping pulses.

Analysis efforts this year focused on (1) demonstrating a new pulse processing technique, dubbed 

multi-pulse fitting, applicable when pulses are poorly 

separated in time but small enough to neglect detector 

response nonlinearity, (2) so-called arrival time corrections, which attempt to adjust for pulse shape 

dependence on photon sub-sample arrival time, due to 

readout nonideality, and (3) work to model nonlinearity 

of detector response, based on a model of detector dynamics governed by a two-dimensional phase space.

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 
44 NIST Applied and Computational Mathematics Division

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

that saturates the detector. A paper presenting these results is in preparation.

Arrival time corrections, made necessary by limitations in the detector readout circuitry that constrain its 

ability to precisely track a fast pulse rise, have challenged, teased, and frustrated analysis attempts of at 

least four members of our project, working separately 

and cooperatively, for more than two years. While repeatable, these nonideal behaviors depend strongly on 

sample rates, pulse magnitudes, and individual detector 

characteristics. Currently they comprise a significant 

fraction of the energy uncertainty. Perhaps improbably, 

one promising approach characterizes and quantifies a 

two-dimensional manifold in fifteen dimensions, for 

each of a few hundred detectors. The character of this 

problem is expected to change significantly with the 

new microwave multiplexers being developed for the 

project on massive detector arrays.

Detector nonlinear response, significant at higher 

photon rates and at energies approaching those that saturate the detectors, remain a challenge. We recently

have retreated to the better characterized, ODEgoverned dynamic response of detectors being developed for HOLMES, a large-scale experiment to 

determine the electron (anti-)neutrino mass (below).

[1] B. K. Alpert, R. D. Horansky, D. A. Bennett, W. B. Doriese, J. W. Fowler, A. S. Hoover, M. W. Rabin, and J. N. 

Ullom, Operation of Gamma-ray Microcalorimeters at 

Elevated Count Rates using Filters with Constraints, Review of Scientific Instruments 84:5 (2013), 056107.

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. In addition to earning NIST a 

place on lists of the most important results in physics 

each of the past three years, they have been used by a 

team that announced in March, 2014, the detection of 

gravity waves. 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. This year new support for 

Innovations in Measurement Science (IMS) was 

awarded to develop both of these capabilities in pursuit 

of 1000-fold increase in sensor throughput, via completely new sensor readout (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, now underway in Italy to measure the 

mass of the electron (anti-)neutrino. This experiment, 

which will use NIST-developed microcalorimeters, 

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 conducted initial simulations, with a novel 

pile-up detection algorithm using NIST detector response models, that convinced the Italian team, led by 

Angelo Nucciotti, to consider a portion of the detector 

design space (for slower pulse rise) previously believed 

unusable for HOLMES. If feasibility is established, the 

resulting detectors would have reduced pulse rise (or arrival time) distortion and the readout electronics 

specifications would be less extreme. Further assessment of this part of the detector design space will rely 

on better elucidation of the detector nonlinear response, 

closely connected with the corresponding characterization for photon high count rate energy resolution.

[1] B. Alpert, M. Balata, D. Bennett, M. Biasotti, C. 

Boragno, C. Brofferio, V. Ceriale, M. De Gerone, R. 

Dressler, M. Faverzani, E. Ferri, J. Fowler, F. Gatti, A. 

Giachero, 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, in 

review.

Stochastic Simulation in Chemical 

Spectroscopy

Anthony Kearsley

William Wallace (NIST MML)

Yutheeka Gadhyan (Pricewaterhouse Coopers)

Analytical chemistry, which has long been a foundation 

of industrial processes, is undergoing a transformation 

as new applications, new instrumentation, and new analytic methods are rapidly being developed and deployed.

Modern applications require information from myriads of different analytical instruments in varying 
Summary of Activities for Fiscal Year 2014 45

formats be synthesized with data from other sources for 

rapid processing. Here, information models must deal 

with the extremely complex problems of fitting, matching, filtering and analysis of structured, semi-structured 

and unstructured data. Very often linear regression or 

“binning” of data is used in conjunction with a derivative checker to find peaks and troughs. Unfortunately, 

this process is fraught with difficulties, making it difficult to reliably automate, and is thus often performed by 

a technician, by eye. This is, of course, simply impossible in many applications (e.g., medicine, forensics) 

where automation is necessary for the instrument to be 

practical. 

Recently we have begun examining the use of stochastic differential equations (SDE) to model and build 

regression simulations of chemical spectra. Very 

loosely, one can construct an SDE that has two components: a drift component that captures a signal and a 

diffusion term that captures the noise. In so doing, the 

SDE naturally (and automatically) can split the instrument output into noise and true signal. Once this has 

been accomplished one can find peaks, examine structures, measure the area under structures, etc. SDE-based 

techniques are quite often used in financial modeling,

albeit in a different way. This year we developed such a 

scheme and have analyzed the convergence and statistical properties of this method. Using a first order EulerMaruyama discretization one can build an inexpensive 

numerical scheme to regress on chemical spectra accurately. Statistical information about the noise can be 

calculated inexpensively. To validate these ideas we derived and analyzed the SDE, and implemented a simple 

numerical integration together with associated convergence analysis that suggested a time-stepping scheme. 

We applied the regression to a data spectrum from a matrix-assisted laser desorption ionization reflectron timeof-flight (MALDI-RTOF) mass spectrometry study of 

narrow-polydispersity synthetic polymer [1]. Results 

appear promising (see Figure 28) as the regression technique outlined in [2] certainly follows the instrument 

output well and succeeds in automatically separating 

noise from signal.

 Because this regression provides a statistical estimate of the noise, one has the ability to interrogate peaks 

in the spectrum, that is, to examine the estimated noise 

in a neighborhood of a peak that was identified by, for 

example, the software from the instrument. In the future 

more specialized problem-dependent selections for kernel type, statistical window-size, and other 

computational details are certain to emerge.

[1] C. M. Guttman, K. M. Flynn, W. E. Wallace and A. J. 

Kearsley, Quantitative Mass Spectrometry and Polydisperse Materials: Creation of An Absolute Molecular 

Mass Distribution Polymer Standard, Macromolecules 42

(2009), 1695–1702. 

[2] A. Kearsley, Y. Gadhyan and W. E. Wallace, Stochastic 

Regression Modelling of Chemical Spectra, Chemometrics and Intelligent Lab. Systems 139 (2014), 26-32. 

Clutter Measurements Pilot Project: 

Toward Evaluating Communications 

Spectrum Sharing Proposals

Bradley Alpert

Chriss Hammerschmidt (NTIA)

Robert Johnk (NTIA)

Jack Wang (NIST ITL)

Formation of the joint NIST and National Telecommunications and Information Administration (NTIA)

Center for Advanced Communications (CAC) and the 

NIST Communications Technology Laboratory (CTL) 

aims to 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 Electromagnetics Division of the NIST PML, the Public Safety

Communications Research (PSCR) of the 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 LTE cell phone path-loss surveys by Johnk, presented by Johnk at the PSCR Public 

Safety Broadband Stakeholder Conference, June, 2014,

NTIA Institue for Telecommunications Sciences (ITS)

lead Hammerschmidt proposed a one-year pilot project

Figure 28. Regression analysis of a data spectrum from a matrixassisted laser desorption ionization reflectron time-of-flight 

(MALDI-RTOF) mass spectrometry study of narrow-polydispersity 

synthetic polymer.
46 NIST Applied and Computational Mathematics Division

to assess communications disruption due to environmental clutter (buildings, vegetation, power lines, etc.). 

Its objectives are to (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 of path loss, and (3) lack of a survey of 

environmental clutter, to serve as a potential independent, predictive variable.

Alpert has proposed denoising of GPS location 

data, based on combining with map data (to reflect travel 

on roads) and a model of vehicle inertia, to significantly 

reduce position uncertainty and improve comparability 

across surveys. The researchers agreed that GPS receivers intended for navigation already incorporate these 

features and ITS will acquire such a receiver and repeat 

some of the surveys. Alpert has proposed using LiDAR 

data, which is openly available for Boulder from a 2010 

survey, as an independent clutter survey. He acquired 

these data and Hammerschmidt is processing them as an 

alternative input (to USGS data) to ITS, in an attempt to 

reconcile with path loss surveys away from cluttered areas. Alpert will also assess whether standard LiDAR 

processing give shape descriptions that might suffice as 

clutter inputs.

Computational Tools for Shape 

Measurement and Analysis

Günay Doğan (Theiss Research)

Javier Bernal

Charles Hagwood (NIST ITL)

Ajay Kannan (Dartmouth College)

Jane Pan (UMBC)

Sharan Arkalgud (Thomas Jefferson High School)

Prashant Athavale (University of Toronto)

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 

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 2014, we made advances in the following specific components of this project.

Shape dissimilarity metrics. We worked with Javier 

Bernal (ACMD) and Charles Hagwood (ITL/SED) to 

develop a fast method to compute the shape dissimilarity 

between closed curves. This is essential for large-scale 

shape analysis and statistics. The basis of our formulation is the elastic shape model of Srivastava et al. [1] 

used to compute geodesic distances between closed 

curves in 2D. This model is invariant with respect to 

translation, rotation, reparameterization, and can handle 

local stretching of curve features easily. The corresponding shape distance matches human intuition of shapes 

well and gives good results in practical applications. The 

downside of this model is that its computational cost is 

cubic with respect to the number of nodes on the given 

curves; it can be very expensive even for moderately

Figure 29. Meshing a synthetic microstructure image. Compare previous result (left) with current result (right).

Figure 30. Illustration of iterative curve evolution for multiphase image segmentation.
Summary of Activities for Fiscal Year 2014 47

sized curves. We reformulated the underlying optimization and obtained an algorithm that is subquadratic in 

computational cost and behaves linearly in practice. Details are provided in a separate section on computation 

of shape geodesics.

Meshing segmented images. We worked with ACMD 

volunteer Ajay Kannan (Dartmouth College) to develop 

algorithms to characterize geometric structures in given 

2D segmented images and to create meshes that exactly 

match the geometry in the images. The algorithm we developed extracts all grains, interfaces and junctions from 

the image and delineates the spatial relationships between them. Moreover it creates a triangulation that 

matches these structures exactly. Our algorithm is completely parameter-free and does not require any tuning

or input from the user other than the segmented image. 

See Figure 29 for an illustration on a synthetic microstructure image.

Image segmentation. We pursued multiple approaches 

to address various image segmentation challenges. We 

implemented a multiphase version of a previous twophase image segmentation algorithm, namely, the ChanVese approach, which uses level set evolution to detect 

region boundaries. Our new model uses a set of 1D

curves to model boundaries of regions with approximately constant image intensity. Previous work in the 

literature requires multiple level set functions for the 

same problem, and requires the number of phases (regions) to be specified in advance, whereas, in our new 

model, this number of phases can change during the execution of the algorithm (see Figure 30 illustrating the 

adaptive segmentation process). Moreover, in order to 

realize robust termination of the iterative algorithm 

without user intervention, we developed a new dynamic 

stopping criterion that is effective under 

various difficult imaging scenarios, i.e. high 

noise, low contrast. 

We developed the following additional

image processing approaches and applications:

Clustering for image segmentation. We 

worked with SURF student Jane Pan to use 

the k-means clustering algorithm as a presegmentation algorithm. We used cluster 

stability analysis to automatically determine 

best clustering results out of several candidates. The combination of total-variation 

denoising and k-means clustering proved to 

be effective for many of the microstructure 

images we considered. See Figure 32 for an 

example of micrograph segmentation with 

this approach. It shows the original microstructure (top-left), clustering with wrong k

= 5 (top-right), clustering without denoising 

(bottom-right), and good clustering after denoising (bottom-right).

Curve initialization for segmentation with junctions. We 

worked on extending the multiphase segmentation algorithm to handle junctions in region boundaries. To be 

able to initialize the extended version of the multiphase 

algorithm, one needs to extract two sets of boundary 

Figure 32. Segmentation of micrograph (top-left) using a combination of total-variation denoising and k-means clustering (bottom-right). Without a good choice of k or 

denoising, the results are not as good (top-right, bottom-left).

Figure 31. An example of enhancement (bottom) of electron 

backscatter data imaging modality (top) with missing pixels (middle).
48 NIST Applied and Computational Mathematics Division

curves from a given labeled image. We pursued this 

problem with SHIP student Sharan Arkalgud. The critical part of this problem was four-coloring of planar 

graphs (or maps). We developed a heuristic algorithm 

that gave promising preliminary results.

EBSD image enhancement. Electron backscatter data 

(EBSD) is an imaging modality that provides the orientation information for a crystal microstructure. It usually 

does not have the full information on a regular grid; 

some measurements might be missing, and some might 

be corrupted with noise. We worked with Prashant 

Athavale (University of Toronto) to develop a regularization algorithm that does both inpainting (completion 

of missing information) and piecewise constant smoothing. The result is very pleasing visually; the grains have 

constant orientation and grain boundaries are smooth (as 

expected from the physics). An example of the enhanced 

EBSD image is shown in Figure 31.

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

Analysis of Elastic Curves in Euclidean Spaces, IEEE 

Transactions on Pattern Analysis and Machine Intelligence 33:7 (2011), 1415–1428.

Computation of Shape Geodesics

Günay Doğan (Theiss Research)

Javier Bernal

Charles Hagwood (NIST ITL)

A major challenge of modern data 

sets is not only their sheer size, but 

also their elements may represent 

complex geometric structures and objects, e.g., proteins, cells, mechanical 

parts, facial surfaces, and other morphologies. Typically, one wants to 

cluster, classify or compare elements 

of such data sets, but performing such 

analyses requires defining a proper 

topological space where these entities 

reside. For data sets of such complex 

elements, the proper space may not be 

linear, thus making it impossible to 

use algorithmic tools designed for Euclidean spaces. This is the case for socalled shape spaces, which have been 

proposed for situations where elements of the data sets represent 

shapes of objects. A powerful shape 

space definition has been proposed by 

Srivastava et al. [1], enabling one to 

compute the elastic shape geodesic 

distance between closed planar 

curves. In [1], curves are considered 

as points in the appropriate Riemannian manifold, in 

which we can define and compute the geodesic distance 

between them. This geodesic distance measure is defined in a way that is invariant to scaling, translation, 

rotation and reparametrization of curves.

We have concentrated on the shape space framework of [1] and have developed a fast algorithm for 

computing the geodesic distance between the shapes of 

two closed curves. Such a fast algorithm is essential for 

large-scale shape analyses. The original algorithm proposed in [1] using dynamic programming has cubic time 

complexity with respect to the number of nodes per 

curve. This is computationally expensive. We propose a 

new fast algorithm whose asymptotic time complexity is 

roughly quadratic but which in our experiments demonstrated subquadratic, almost linear growth in running 

times depending on the type of curve data [2].

Mathematically, the shape distance computation is 

formulated as a global optimization over triplets of starting points, rotations and reparametrizations. With the 

starting point and rotation fixed, our algorithm computes 

a globally optimal reparametrization. For this, we developed a very fast iterative nonlinear constrained 

optimization algorithm initialized by the solution of a 

fast dynamic programming algorithm. The resulting 

reparametrization algorithm is plugged into another procedure of outer iterations that computes the optimal 

starting point and rotation separately. This separate optimization if done in the common naive way has 

quadratic time complexity as it takes place by looping 

through each node in one of the two curves. Recently, 

Figure 33. Distance matrix of MPEG7 shape set.
Summary of Activities for Fiscal Year 2014 49

we developed a new algorithm for this based on the Fast 

Fourier Transform (FFT) that has O(N log N) complexity, where N is the number of nodes per curve. This 

resulted in an order of magnitude speed-up for the computation of the optimal starting point and rotation in our 

experiments. Accordingly, we found that our method for 

calculating accurate shape distance values, based on our 

new algorithms for computing optimal starting points, 

rotations and reparametrizations, does this at a fraction 

of the computational cost of previous approaches.

An illustration of our results with the MPEG7 shape 

data set is given in Figure 33, which provides a graphical 

illustration of the pairwise distances between 100 shape 

examples from the MPEG7 shape data set. For this example, we chose ten shape categories (apple, bat, beetle, 

bell, bone, bottle, brick, camel, car, carriage) and ten 

curve examples per category, resampled the curves at 

N=256 nodes, and computed the geodesic shape distances between the 100×100 pairs. As expected, the 

shape distances between curves in the same category, 

shown in the diagonal blocks, were smaller (appear 

darker in the figure), and the shape distances between 

curves from different categories, shown in off-diagonal 

blocks, were larger (appear brighter in the figure). We 

compared the original geodesic shape distance algorithm from [1] with our new algorithm. The original 

algorithm computed 100×100 distances in 129 hours, 

whereas our new algorithm computed the same distance 

matrix in 12.5 hours, a speed-up factor of 10. When the 

curves have more nodes, the speed-up is even more dramatic. For example, for curves with N=1024, our 

algorithm can be 50-1000 times faster than the original 

algorithm.

[1] A, 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. Hagwood, A Fast Algorithm 

for Elastic Shape Distances between Closed Planar 

Curves, in review.

Neural Networks for Cell Feature 

Identification

Javier Bernal

Jose Torres-Jimenez (CINVESTAV, Mexico)

A backpropagation algorithm has been implemented for 

training neural networks to be used for the identification 

of subcellular features in cell images relevant to cell biologists. Approaches exist for recognizing objects or 

pattern classes associated with an image based on the 

use of sample patterns (training patterns) to estimate statistical parameters of each pattern class. However the 

statistical properties of the pattern classes might not be 

known or might be difficult to estimate. Therefore, the 

neural network approach that produces the required decision functions based solely on training without 

assumptions about probability density functions associated with the pattern classes may be more successful.

A neural network is a computational model that 

consists of computing elements called “neurons” organized as a network, reminiscent of the way in which 

neurons are believed to be interconnected in the brain. It 

is an adaptive system that changes its structure based on 

information that flows through the network during a 

training phase. It is mostly used for modeling relationships between input and output data and for partitioning

data into classes.

During training with the backpropagation algorithm 

the average squared error between the networks’ output 

and a target value is minimized for each point or pattern 

(in d-dimensional space) in the training set. Via training, 

coefficients of decision functions are obtained and associated with neurons in the network. Once the training is 

done other data points or patterns are put through the 

network and assigned to a class according to the output 

obtained. For our purposes the resulting implementation 

will be used for identifying pattern classes in d-dimensional space as each pixel in an image is associated with 

a d-dimensional pattern, the coordinates of the pattern 

corresponding to d distinct attributes associated with the 

pixel.

Since training a neural network as described is 

equivalent to minimizing an error function of several 

variables (weights in the network), a scaled conjugate 

gradient method (SCGM) has been implemented for this 

purpose as part of our backpropagation algorithm.

However, as the convergence of the weights with 

the SCGM can be slow at times during training, it is apparent that a hybridization of the SCGM and a 

metaheuristic algorithm such as the simulated annealing 

may be the way to alleviate this problem. Accordingly,

an implementation of the simulated annealing algorithm 

to be used in tandem with the SCGM is underway.

Stable Explicit Time Marching in 

Well-posed or Ill-posed Nonlinear 

Parabolic Equations

Alfred S. Carasso

Significant progress has been made on stabilizing pure 

explicit time differencing in the numerical computation 

of multidimensional nonlinear parabolic equations on

rectangular regions [4]. Explicit schemes are highly desirable because of their simplicity, but such schemes are 

seldom used as they entail prohibitive Courant stability 

restrictions on the time step ∆t. Rather, unconditionally 

stable implicit schemes are commonly used, requiring 
50 NIST Applied and Computational Mathematics Division

computationally intensive solutions of the resulting algebraic systems of difference equations at each time 

step. The present stabilized explicit scheme uses 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 FFT algorithms. The stabilized 

explicit scheme requires no Courant restriction on the 

time step ∆t, and is of great value in computing wellposed forward parabolic equations on fine meshes, by 

simply lagging the nonlinearity at the previous time step. 

Such stabilization leads to a distortion away from the 

true solution. However, that error is often small enough 

to allow useful results in many problems of interest

For ill-posed backward parabolic equations, all 

stepwise time marching algorithms, whether explicit or 

implicit, are necessarily unconditionally unstable. However, the stabilized explicit scheme is stable even when 

run backward in time. This opens the door to relatively 

easy and useful computation of multidimensional nonlinear backward parabolic equations, a category of 

problems that is widely believed to be intractable. The 

method complements the Quasi-Reversibility Method 

[5, 8], whose formulation is primarily oriented toward 

linear problems. There is considerable interest in such 

backward reconstructions, notably in the developing 

field of environmental forensics [3, 8], where contaminant transport is often modeled by parabolic advection 

dispersion equations [6, 7]. However, the class of nonlinear problems that can be handled by the present 

method is limited, although it is significant.

Let L be a linear autonomous second order elliptic 

differential operator with smooth variable coefficients in 

a rectangular region Ω in R

n

, with homogeneous Dirichlet or Neumann boundary conditions on ∂Ω. Let ǁ ǁ2

denote the norm on L

2

(Ω). The stabilized scheme involves the following assumption regarding the 

semigroups generated by –(–∆)pand (L

*L)q/2 : Given 

any ω > 0, and q with 1 < q ≤ 3, there exist constants Γ, 

ε > 0, and p ≥ q, such that for all g ε L

2

(Ω) and sufficiently small time step ∆t,

Figure 35. Useful computation of well-posed forward nonlinear parabolic problems on 512×512 mesh, using stabilized explicit scheme with a 

value of ∆t that is unstable in the uncompensated pure explicit scheme.

Figure 34. Backward recovery from nonlinearly blurred data in 

512×512 Liz Taylor image, using stabilized explicit scheme with Γ = 

1.0, ε = 7.5×10-8, p = 2.735. Van Cittert procedure develops instabilities after 8 iterations.
Summary of Activities for Fiscal Year 2014 51

‖ exp{−ε Δt (−Δ)

p} g ‖2

≤ Γ ‖ exp {−ω Δt (L

∗L)

q

2} g‖

2

(1)

Results similar in nature to Eq. 1 are known in the deep 

theory of Gaussian estimates for heat kernels [1, 2]. In 

applications to nonlinear parabolic equations ut = Pu, the 

operator L in Eq. 1 is assumed to be a useful linear approximation to the nonlinear elliptic operator P. 

Stabilization of the explicit scheme requires the selection of constants ε > 0, p > 1, and Γ > 0, together with 

subsequent interactive adjustment of these parameters 

based on prior knowledge about the solution. Having 

located a useful triple (ε, p, Γ), it is shown in [4] that a 

useful error bound can be obtained in terms of the parameters ω and q in the inequality in Eq. 1.

Fictitious nonlinear parabolic blurring and deblurring of 512×512 pixel images provide instructive 

mathematical examples. Underlying these images are 

highly irregular and jagged intensity surfaces, and these 

data can severely test potentially unstable computational

algorithms. In Figure 35, useful results are obtained in 

a well-posed forward nonlinear parabolic equation using

the stabilized explicit scheme with a time step ∆t 10 

times larger than required by the Courant condition. In 

Figure 34, useful backward in time reconstruction from 

severe nonlinear blurring is achieved. Moreover, in that 

problem, the computationally intensive Van Cittert iteration [9] becomes unstable after 8 iterations.

[1] W. Arendt and A. F. M. ter Elst, Gaussian Estimates for 

Second Order Elliptic Operators with Boundary Conditions, Journal of Operator Theory 38 (1997), 87-130.

[2] D. G. Aronson, Bounds for the Fundamental Solution of 

a Parabolic Equation, Bulletin of the American Mathematical Society 73 (1967), 890-896.

[3] 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.

[4] A. S. Carasso, Stable Explicit Time Marching in WellPosed or Ill-Posed Nonlinear Parabolic Equations, 

NISTIR 8027, October 2014.

[5] R. Lattès and J. L. Lions, The Method of Quasi-Reversibility, American Elsevier, New York, 1969.

[6] J. D. Logan, Transport Modeling in Hydrogeochemical 

Systems, Springer, New York, 2001.

[7] R. N. Singh, Advection Diffusion Equation Models in 

Near-surface Geophysical and Environmental Sciences, 

Journal of the Indian Geophysical Union 17 (2013), 117-

127.

[8] 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.

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

Intensitätsverteilung in Spektrallinien II, Zeitshrift für 

Physik 69 (1931), 298-308.

Traceable Simulation of Magnetic 

Resonance Imaging

Zydrunas Gimbutas

Andrew Dienstfrey

Steve 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 mm2s

-1

, and temperature in K. However, as of a few years ago the use of SI 

units for these technologies was potentially unwarranted

as SI traceability chains supporting these MRI measurement modalities were unclear if not non-existent. More 

recently NIST and partners have made substantial investments to develop such traceability chains. In the 

medical community, standard reference artifacts are referred to as phantoms and, in particular, NIST now

supports several phantoms providing SI-traceable calibration artifacts for MRI scanners.

MRI is governed by solutions to 

dM

dt

= γM × B −

Mxx̂ + Myŷ

T2

+

(M0 − Mz)ẑ

T1

+D∇

2M

known as the Bloch equations. Here M the magnetic moment arising from collections of nuclear spins, the 

gyromagnetic ratio γ is a physical constant, and B is the 

forcing magnetization. The quantities of medical interest 

are T1, T2 and D. The first two are tissue-dependent relaxation times. Experimental estimation of these times 

provides a two-parameter characterization of the material exhibiting the signal. This is the source of MRI's 

unparalleled capabilities for in vivo soft-tissue imaging. 

Moreover, D is an effective diffusion constant that reflects a combination of tissue porosity and anatomical 

structure. Refined control of the forcing function B using combinations of linear gradients and RF fields

allows one to map distributions of T1, T2 and D. The details are numerous. The point of this brief discussion is 

to demonstrate that, while extremely challenging, predictive quantitative simulation of this imaging modality 

is nevertheless possible!

Virtual prototyping is highly desirable to improve 

the fundamental understanding of MRI capabilities resulting in significant reductions in time and costs to 

develop new scan technologies. A growing number of 

computer codes are available which claim to do just this. 

While there is uniform agreement on the potential for 

quantitative MRI simulation, neither NIST nor any other 

national metrology institution is currently positioned to 

certify the accuracy of such claims.
52 NIST Applied and Computational Mathematics Division

In 2014 we developed an elementary MRI simulator 

to serve as the foundation for what we ultimately expect 

to become the computational reference for this community [1]. The NIST Bloch solver is parallelizable via 

OpenMP and includes several commonly used MRI sequences such as the gradient echo and spin echo

sequence families, in both one and two dimensions, optionally combined with the inversion recovery step. We 

have also developed a new numerical scheme for acceleration of decaying exponential sums due to T2 effects 

which allows much faster simulations of the received 

MRI signals. The method is based on the observation 

that the rates of T2 are uniformly bounded within biomedical tissues of interest, therefore, over a finite 

measurement time the system of all possible signals can 

be compressed. For implementation efficiency, the proposed method is based on the interpolative 

decomposition of real decaying exponentials combined 

with the discrete Fourier transform. The interpolation 

basis of received MRI signals, interpolation nodes for 

time sampling, and signal scaling factors can all be precomputed, yielding a fast scheme involving a small 

number of the discrete (in general, non-uniform) Fourier 

transforms. A technical report is in preparation.

We have completed preliminary validations of the 

simulation results by comparison against measurements 

of T1 and T2 array phantoms provided by the MRI group 

at NIST. We are currently testing accuracy, performance, and comparing the simulation capabilities of 

several widely available MRI simulators and tools, such 

as SIMRI, JEMRIS, and ODIN [5-7]. In particular, 

quantitative error analysis of SIMRI simulator is under 

investigation. Such comparisons may serve as templates 

for the future computational benchmark problems.

In addition to virtual prototyping, there exist many 

research opportunities directly arising from experimental MRI signals analysis. In medical practice, 

quantitative measurement of T1 and T2 is useful for a 

wide range of assessments including: iron distribution in

the brain which may serve as a biomarker for traumatic 

brain injury (see below), treatment monitoring for heart 

attacks, and multiple sclerosis [8]. These are just a few 

examples. In fact, the prospects for patho-physiological 

assessment enabled by quantitative-MRI are nearly limitless. The tradeoffs associated with this are time, cost, 

and accuracy. Together with the MRI measurement

group at NIST, we are investigating T1 and T2 curve 

mapping techniques that use complex MRI signal data

[2-4]. The new schemes compare favorably to the existing techniques that use only the magnitude of

reconstructed MRI signal. For given accuracy, we expect a reduction in the number of MRI scans to be 

collected due to reduced numerical ranks of the fitting 

curves and possible use of model linearization. We have 

also discussed possibilities of developing non-linear 

gradient and phase error correction for the current NIST 

MRI measurement system.

A future line of investigation is exploring possibilities for quantitative measurement of the magnetic 

moment of local iron distribution. This distribution is 

suspected to be an important bio-marker for brain function, and irregularities that have been associated with 

traumatic brain injury. It is proposed that magnetic moments can be mapped by phase measurement of MRI 

signals. Figure 36 shows one such measurement. The 

image on the left reveals a heavily-wrapped phase image. The linear oscillation of phase across the image is 

the result of an offset of the k-space acquisition data. We 

have developed an analysis which estimates and corrects 

for this offset. The result is shown in the image on the 

Figure 36. The phase of the MRI signal as measured by the scanner contains a k-space offset. This results in the linear plane wave oscillation 

of phase shown in the image on the left. The right image shows this same phase measurement after applying the new correction analysis 

performed by NIST. This correction will allow for more detailed mapping of the distribution of magnetic moments in the future.
Summary of Activities for Fiscal Year 2014 53

right. Correcting for this large systematic background 

effect will allow for more fine-scale analysis of magnetic moment distribution in the future.

[1] Z. Gimbutas and A. Dienstfrey, “MRI Simulators and 

their Performance”, NIST Workshop on Standards for 

Quantitative MRI, July 14-17, 2014, NIST, Boulder, Colorado.

[2] N. Stikov, M. Boudreau, I. R. Levesque, C. L. Tardif, J. 

K. Barral, G. B. Pike, N. Stikov, et al., On the Accuracy 

of T1 Mapping: Searching for Common Ground, Magnetic Resonance in Medicine, Feb 27, 2014.

[3] P. B. Kingsley, Signal Intensities and T1 Calculations in 

Multiple-Echo Sequences with Imperfect Pulses, Concepts in Magnetic Resonance 11:1 (1999), 29-49.

[4] P. B. Kingsley, Methods of Measuring Spin-Lattice (T1)

Relaxation Times: An Annotated Bibliography, Concepts 

in Magnetic Resonance 11:4 (1999), 243-276.

[5] H. Benoit-Cattin, G. Collewet, H. Saint-Jaimes and C.

Odet, The SIMRI Project: a Versatile and Interactive MRI 

Simulator, Journal of Magnetic Resonance 173:1 (March 

2005), 97-115.

[6] T. H. Jochimsen and M. von Mengershausen, ODIN - Object-oriented Development Interface for NMR, Journal of 

Magnetic Resonance 170:1 (September 2004), 67-78.

[7] T. Stöcker, K. Vahedipour and D. Pugfelder, High-Performance Computing MRI simulations, Magnetic 

Resonance in Medicine 64:1 (July 2010), 186-193.

[8] H.-L. Cheng, et al, Practical Medical Applications of 

Quantitative MR Relaxometry, Journal of Magnetic Resonance Imaging 36 (2012), 805-824.

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)

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 focused on hp-adaptive methods where 

adaptivity is in both the grid size and the polynomial order of approximation, resulting in exponential rates of 

convergence. W. Mitchell has been developing a code, 

PHAML, to apply these methods on parallel computers. 

The expertise and software developed in this project are 

useful for many NIST laboratory programs, including 

material design, semiconductor device simulation, the 

quantum physics of matter, and simulation of scanning 

electron microscopes.

 Recently we completed a study of the performance 

of 13 proposed hp-adaptive strategies in terms of accuracy vs. degrees of freedom and computation time vs. 

degrees of freedom. A paper presenting the results of 

this experiment appeared in ACM Transactions on 

Mathematical Software this year. For this experiment 

we gathered a collection of 12 test problems, most of 

which came from the numerical results section of papers 

on hp-adaptive refinement. These problems contain a 

variety of difficulties including singularities, sharp 

peaks, wave fronts, oscillations and boundary layers. 

Most of them are parametrized to adjust the strength of

the difficulty. We found that the strategy which is most 

effective depends on the type of difficulty and the accuracy requirements. The so-called reference solution 

methods performed well in terms of accuracy vs. degrees of freedom, but are very expensive 

computationally. In terms of accuracy vs. computation 

time, the use of a priori knowledge is best for problems 

with known singularities and no other significant feature, while the method based on the decay rate of the 

coefficients of the p-hierarchical basis seems to be the 

best general purpose strategy.

 The 12 test problems used in the study are all 2D 

linear elliptic PDEs. We believe it would be useful to 

create a collection of standard benchmark PDEs, appropriate for adaptive mesh refinement, of other types, 

including 3D, parabolic, hyperbolic, nonlinear, etc. We 

have created a web site [1] to make such a collection 

available to the research community. This year we made 

improvements to the design of the web site and added 

15 more benchmark problems. The new problems include 1D, 3D, nonlinear, and parabolic problems.

There are three major collaborative efforts with PML 

to 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. Previously we calculated the bound states, 

scattering properties and dynamics of two dipolar 

molecules held in a cylindrically symmetric trap, a 

2D problem. We have extended these simulations 

to a 3D model without the assumption of cylindrical 

symmetry. This year we demonstrated that PHAML 

can be used to perform experiments to see how varying the parameters of a simulation affects the 

energy levels and wave functions. We performed 

computations with the 3D model of the interaction 

of two trapped RbCs dipoles in which we varied (1) 

the strength of the dipolement, and (2) the angle between the dipoles. Figure 37 shows how the first ten 
54 NIST Applied and Computational Mathematics Division

eigenvalues (energy levels) change as the strength 

of the dipole moment varies from 0.125 to 0.25 D.

 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. 

Villarrubia has a code 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 validated the use of PHAML for this 

application by comparing results with GetDP, the 

finite element program that was previously used. 

We performed several performance enhancements 

for this application and obtained a 5-fold speedup 

over GetDP. We also extended PHAML to handle 

floating constraints, which occur when the sample 

contains a stray piece of metal.

 We have begun a new collaboration with Garnett 

Bryant to apply PHAML to the simulation of quantum dot structures. Nanoscale semiconductor 

quantum dot structures can be modified, controlled, 

and manipulated by applied electric fields that arise 

from the local strain in the quantum dots. In this 

collaboration we will use PHAML to determine 

these applied fields and potentials down to the scale 

of the quantum dots. PHAML will be interfaced as 

needed with existing codes that are being used to 

describe these quantum dot structures.

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 on NIST applications.

[1] NIST Adaptive Mesh Refinement Benchmark Problems, 

http://math.nist.gov/amr-benchmark.

[2] 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).

[3] W. F. Mitchell, A Collection of 2D Elliptic Problems for 

Testing Adaptive Algorithms, Applied Mathematics and 

Computation 220 (2013), 350-364.

[4] W. F. Mitchell, “Recent Advances in PHAML,” SIAM 

Conference on Parallel Processing for Scientific Computing, Portland, OR, February 2014.

[5] W. F. Mitchell and M. A. McClain, “Performance of hpAdaptive Strategies for Elliptic Partial Differential Equations,” International Conference on Spectral and High 

Order Methods, Salt Lake City, UT, June 2014.

[6] 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.

Numerical Solutions of the TimeDependent Schrödinger Equation 

Barry I. Schneider

Klaus Bartschat (Drake University)

Xiaoxu Guan (Drake University)

Johannes Feist (Universidad Autónoma de Madrid)

Stefan Nagele (Vienna University of Technology)

Joachim Burgdörfer (Vienna University of Technology)

Renate Pazourek (Louisiana State University)

We have been collaborating for a number of years to develop numerically robust methods for solving the timedependent Schrödinger equation. Although the methods 

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 s) pulses provide a new window to study the 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.) These processes can only be described 

using time dependent quantum mechanics and, where 

appropriate, need to be coupled to Maxwell’s equations. 

At the end of the day, we wish to image quantum phenomena with subfemtosecond temporal and subAngstrom spatial resolution. Eventually, one can contemplate producing “molecular movies” of this motion 

in much the same way as it is done in molecular dynamics simulations of heavy particle processes. 

Figure 37. Effect of the strength of the dipole moment on the first 

ten eigenenergies of a model of two trapped RbCs molecules.
Summary of Activities for Fiscal Year 2014 55

The basic methodology as applied to atoms and 

simple diatomic molecules, has been described in [1-3] 

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 

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 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.

During the past year, the group has concentrated its 

efforts on describing the H2 molecule when exposed to 

radiation parallel and perpendicular to the internuclear 

axis. These studies provide benchmark calculations 

which may be used by others to test their numerical approaches. The calculations, described in [5-6], show 

quite different behavior from one another. This is a consequence of the difference in the intermediate excited 

states populated by the orientation of the radiation field 

with respect to the internuclear axis. In the parallel geometry, the very long-lived double excited states of H2 

require quite long pules to resolve the dynamics as the 

quantum state evolves in time while the perpendicular 

geometry is essentially insensitive to the length of the 

pulses. In Figure 38 we compare the current calculations 

in the perpendicular and parallel geometry with some 

others. The calculations show excellent agreement with 

other time-dependent approaches but disagree with calculations using time-independent methods. Resolving 

the detailed dynamics of these double excited states remains a computational challenge and the role of the 

pulses, particularly their length, is critical to understanding the physics. 

Future developments will extend the methodology 

to polyatomic molecules and examine more efficient 

methods of propagating the wavefunction in time. In addition, there will be some effort to examine other partial 

differential equations to determine the generality of the 

approach beyond the current application to intense, short 

radiation.

[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, K. Bartschat, B. I. Schneider, L. Koesterke, 

Resonance Effects in Two-Photon Ionization of H2 by 

Femtosecond XUV Laser Pulses, Physical Review A 88 

(2013), 043402.

[6] 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. 

Figure 38. Generalized total cross section for two-photon double 

ionization of the H2 molecule. In the upper panel, the molecular axis 

is oriented perpendicular to the linear polarization vector (represented by a double-headed arrow) of the laser pulse. Our present 

results were obtained for pulse lengths of 10, 20, and 30 optical 

cycles. Also shown are the ab initio and the model results of Simonsen et al., as well as the cross sections of Colgan et al. and Morales 

et al. at 30 eV. The lower panel shows a comparison between our 

ab initio results obtained in the perpendicular and parallel geometries, with the corresponding predictions from a simple model 

suggested by Simonsen.
56 NIST Applied and Computational Mathematics Division

Equilibrium and Stability of Liquid

Drops on a Conical Substrate under 

Gravity

Asha K. Nurse

Sean Colbert-Kelly

Geoffrey B. McFadden

Sam R. Coriell (NIST MML)

Capillary forces lead to a rich collection of problems in 

physics, chemistry, and materials science that have both 

beauty and technological importance [1]. Shapes such as 

soap films, drops, and bubbles display interesting dynamical and equilibrium behavior, and have been 

studied in a variety of settings (see, e.g., the review articles [2, 3] and references therein). 

Here we study the equilibrium and stability of an 

axisymmetric liquid drop that is resting on the side of a 

conical solid substrate under the combined effects of 

capillarity and gravity. This study is motivated by recent 

experimental observations of the behavior of clusters of 

biological cells that self-assemble at the bottom of patterned containers [4, 5]. Each compartment of the 

partitioned container includes a conical obstruction in its 

base that interrupts the tissue assembly, leading to toroidal clusters of cells at the base of each cone. After 

assembly, a cell cluster is often observed to climb up the 

side of the cone. 

A possible mechanism for this dynamical behavior 

is based on the interplay of capillarity and gravitational 

forces: a toroidal tissue cluster would like to reduce its 

surface area, which it can do by reducing its major radius 

(the long way around the torus) by moving to higher positions on the cone. In climbing the cone the 

gravitational potential energy of the sample is increased, 

so the dynamical process must balance both forms of energy. A model of the dynamical process based on 

toroidally-shaped clusters evolving by surface diffusion 

has been used [4] to interpret the experimental observations, which occasionally included both tilting of the cell 

cluster relative to the cone axis (see Figure 39), and the 

development of fluted distortions in the azimuthal direction.

In the light of these interesting experiments it seems 

desirable to consider the simpler problem of determining 

the equilibrium and stability of liquid drops on a conical 

substrate. We formulate a variational statement of the 

problem in terms of an energy functional containing 

both surface energy and gravitational potential energy 

contributions subject to a volume constraint. Axisymmetric stationary shapes that extremize the energy then 

satisfy the Laplace-Young equation that represents the 

local balance of capillary, gravitational, and pressure 

forces at each point of the interface. Appropriate natural 

boundary conditions at the contact line where the drop, 

substrate, and surrounding fluid meet also follow from 

the variational principle, yielding the familiar Young 

boundary condition that determines the drop’s contact 

angle at the trijunction. The second variation of the energy functional is examined numerically to determine 

the linear stability of the equilibrium shapes. Among the 

results, we find that the equilibrium shapes are often unstable to non-axisymmetric perturbations that produce 

tilting of the toroid relative to the cone axis; an example 

is shown in Figure 40. We also find a broad class of instabilities that resemble the Rayleigh instability that is 

responsible for the break-up of a cylindrical liquid jet 

into droplets whose radius is roughly that of the jet’s circumference. This work has been submitted for 

publication [6] and is currently undergoing revision to 

address referee comments. A related paper is undergoing review [7].

[1] Pierre-Gilles de Gennes, Francoise Brochard-Wyart, and 

David Quere, Capillarity and Wetting Phenomena: 

Figure 39. Side view of a toroidal cluster of biological cells climbing the side of a conical obstacle in a patterned substrate [5]. The 

right hand side of the cluster is slightly higher than the left hand 

side, suggesting a possible asymmetric instability of an axisymmetric configuration.

Figure 40. Numerical calculation of the axisymmetric equilibrium 

shape (blue curve) and the asymmetric perturbed shape (red curve) 

producing a tilted drop [6]. Here gravity is in the downward direction, the half-angle of the cone is 35 degrees and the contact angle 

of the drop is 90 degrees.
Summary of Activities for Fiscal Year 2014 57

Drops, Bubbles, Pearls, Waves (Springer, Berlin, 2004).

[2] H. M. Princen, The Equilibrium Shape of Interfaces, 

Drops, and Bubbles: Rigid and Deformable Particles at 

Interfaces, in Surface and Colloid Science 2, (Egon Matijevic, ed.), Wiley-Interscience, New York, 1969, 1-84.

[3] D. H. Michael, Meniscus Stability, Annual Review of 

Fluid Mechanics 81 (1981), 189-215.

[4] A. Nurse, L. B. Freund and J. Youssef, A Model of Force 

Generation in a Three-dimensional Toroidal Cluster of 

Cells, Journal of Applied Mechanics 79 (2012), 051013.

[5] J. Youssef, A. K. Nurse, L. B. Freund and J. R. Morgan, 

Quantification of the Forces Driving Self-assembly of 

Three-dimensional Microtissues, Proceedings of the National Academy of Sciences 108 (2011), 6993-6998.

[6] 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, in review.

[7] A.K. Nurse, S.R. Coriell and G. B. McFadden, On the 

Stability of Rotating Drops, in review.

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 are currently 

participating in a benchmarking exercise to compare the 

simulation results produced by a number of codes that 

are in use by the fusion community [1, 2]. The benchmark is based on the DIII-D tokomak experiment at 

General Atomics in San Diego, California. We are evaluating the NSTAB equilibrium and stability code 

developed by Paul Garabedian and Mark Taylor at NYU 

[3], which uses a variational formulation of the equations of magneto-hydrodynamics to compute plasma 

equilibria that exhibit a family of nested flux surfaces 

that enable plasma containment [4]. The benchmarking 

exercise is being organized by researchers at the Princeton Plasma Physics Lab and Oak Ridge National 

Laboratory.

[1] A. Reiman, A. Cerfon, G. McFadden, et al., Tokamak 

Plasma High Field Side Response to a n=3 Magnetic Perturbation: A Comparison of 3D Equilibrium Solutions 

from Seven Different Codes, in review.

[2] A. Reiman, A. Cerfon, G. McFadden, et al., A CrossBenchmarking and Validation Initiative for Tokamak 3D 

Equilibrium Calculations, in Proceedings of the 25th 

IAEA Fusion Energy Conference (AEA CN-221), St. Petersburg, Russia, 13-18 October 13-18, 2014.

[3] M. Taylor, A High Performance Spectral Code for Nonlinear MHD Stability, Journal of Computational Physics

110 (1994), 407-418.

[4] P. R. Garabedian and G. B. McFadden, Design of the 

DEMO Fusion Reactor Following ITER, Journal of Research of the NIST 114 (2009), 229-236.

Design-Basis Hurricane Winds and 

Missiles for Nuclear Power Plants

Florian A. Potra

Emil Simiu (NIST EL)

Brad Harvey (Nuclear Regulatory Commission) 

Kevin Quinlan (Nuclear Regulatory Commission)

To ensure the safety of nuclear power plants in the event 

of a hurricane strike, U.S. Nuclear Regulatory Commission (NRC) regulations require that nuclear power plant 

designs consider the impact of hurricane-generated missiles in addition to the direct action of the hurricane 

wind. Hurricanes are capable of generating missiles 

from objects lying within the path of the hurricane wind 

and from the debris of nearby damaged structures. Protection from a spectrum of missiles (ranging from a 

massive missile that deforms on impact to a rigid penetrating missile) provides assurance that the structures, 

systems, and components important to safety will be 

available to mitigate the potential effects of a hurricane 

on plant safety.

The implementation of the Enhanced Fujita Scale in 

2007 by the U.S. National Weather Service resulted in 

decreasing the design-basis tornado wind speeds suggested by the NRC. With the reduction of the designbasis tornado wind speeds, it was no longer clear that the 

revised design-basis tornado wind and missiles would 

bound the design-basis hurricane wind and missiles in 

all areas of the United States. This prompted studies into 

extreme wind gusts during hurricanes and their relationship to hurricane missile speeds. The study of missile 

speeds during hurricanes concluded that, because of assumed differences between the tornado and hurricane 

wind fields, airborne missiles can fly faster in a hurricane wind field having the same 3 second gust wind 

speed at 10 meters (33 feet) above terrain with open exposure as a tornado wind field. 

Figure 41 presents the resulting map for hurricane 

wind speeds with annual exceedance probabilities of 

10-7. These wind speeds are representative of a 3 second

peak gust wind speed at a height of 10 m (33 feet) above 

ground in flat open terrain, which is consistent with the 

definition of Exposure C in ASCE/SEI 7-05. 
58 NIST Applied and Computational Mathematics Division

Figure 42 shows locations that have design-basis 

hurricane wind speeds higher than the recommended design-basis tornado wind speeds. Along the Gulf and 

southern Atlantic coastlines, the hurricane-induced wind 

gusts can be higher than the regionalized gusts produced 

by tornadoes. 

The resulting automobile and schedule 40 pipe horizontal missile speeds as derived from the analysis 

presented in NUREG/CR-7004 [1] and as incorporated 

into RG 1.221 are plotted in Figure 43. The NRC considers the design-basis hurricane missiles to be capable 

of striking in all directions with the horizontal speeds 

shown in Figure 43 and with a vertical speed of 26 m/s 

(58 mph). The horizontal hurricane missile speeds 

shown in Figure 43 represent maximum horizontal missile speeds in open terrain. 

New numerical simulations show that airborne missiles can fly faster in a hurricane wind field than 

previously assumed. The results have been submitted recently for publication [2]. Further simulations with 

improved models are planned in the future.

[1] E. Simiu and F. A. Potra, Technical Basis for Regulatory 

Guidance on Design-Basis Hurricane Borne Missile 

Speeds for Nuclear Power Plants, NUREG/CR-7004, 

U.S. Nuclear Regulatory Commission, Washington, 

D.C., 2011.

[2] B. Harvey, E. Simiu, F. A. Potra, K. Quinlan and N. 

Chokshi, Design-basis Hurricane Winds and Missiles for 

Nuclear Power Plants, in review.

Algorithm Development and 

Uncertainty Quantification in 

Tomographic Radiation Transport 

Applications

Anthony Kearsley

Walid Keyrouz (NIST ITL)

Zachary Levine (NIST PL)

Adam Pintar (NIST ITL)

Radiation transport underlies many measurement techniques used at NIST and around the world. Examples 

include x-ray tomography, electron tomography, neutron tomography, and optical scattering for radiometry 

and medicine. The measurements of interest in radiation 

transport problems are the solutions to inverse problems. 

A source emits radiation, the radiation travels through a 

sample, and detectors observe the radiation afterward. 

Based on noisy observations, the properties of the sample, which are the quantities of interest, are inferred. 

Since the reconstructions are based on noisy data, the 

reconstructions are only estimates of the true sample 

properties. If another dataset was observed under the 

same conditions, the result would be different, and so 

too would the reconstruction. 

An example of this problem is Greenhouse Gas Sequestration Monitoring (GGSM) (see Figure 44). Any 

carbon sequestration effort must be massive in scale to 

produce a noticeable effect in the amount of carbon dioxide released. It will be important to employ wide-scale 

automated systems to monitor for leaks; otherwise, the 

entire effort is in vain. Establishing the feasibility of 

such monitoring by analyzing Dual Optical Absorption 

Spectroscopy (DOAS) measurements with a pseudotomographic approach is a goal of researchers in this 

area. Uncertainty quantification is especially important 

Figure 41. Design-basis hurricane peak-gust wind speeds in mph 

(m/s) at 10-m height in flat open terrain, annual exceedance probability of 10-7

(from Figure 3-4 of NUREG/CR-7005).

Figure 42. Locations where design-basis hurricane wind speeds 

exceed those for tornadoes, annual exceedance probability of 10-7

(from Figure 3-6 of NUREG/CR-7005).

Figure 43. Maximum horizontal speeds for the design-basis hurricane and tornado automobile and schedule 40 pipe missiles.
Summary of Activities for Fiscal Year 2014 59

when the data are information-poor because the estimated location of the leak may be quite far from the 

actual location. These situations can arise when relatively few measurements are made, or the leak is slow 

and the plume concentration is difficult to detect (see 

Figure 45). 

Radiation transport models predict what detectors 

will observe under an assumed set of underlying conditions, i.e., a sample property or measurement of interest. 

To estimate the underlying conditions, they may be adjusted until there is good agreement between the 

predictions and the observations. The observations follow statistically independent Poisson distributions, 

where the Poisson mean is provided by the combination 

of the radiation transport model and the plume model. 

There is ample prior information about the underlying 

conditions since some parameters of the plume model 

such as the wind velocity may be measured separately. 

Our work has examined formulating objective functions using point estimation and uncertainty 

quantification. These two things are linked by a posterior distribution. The point estimate will be the mode of 

the posterior distribution, i.e., the underlying condition 

with the highest probability given the observed data. 

There are other reasonable point estimates such as the 

posterior mean or median, but in cases where the information content of the data is high all three should be 

similar. Standard uncertainties are taken from the covariance matrix of the posterior distribution, and posterior 

intervals (regions in more than 1D) cover a specified 

amount of posterior probability (say 95 %).

We have also begun working on specialized optimization algorithms tailored to radiation transport 

problems. In situations where one wishes to optimize a 

“bumpy” function, the extent of the “bumpiness” is often caused by noise. Here it appears that there are two 

sources of noise. The data are noisy realizations of the 

predictions, and thus contain incomplete information 

about the nature of the true underlying conditions. Also, 

to realize a set of predictions from radiation transport 

models, Monte Carlo calculations are required, so the 

predictions themselves are noisy. 

Robust and Efficient Optimization 

for Simulating Building Energy 

Usage 

Anthony Kearsley 

Amanda Pertzborn (NIST EL)

Jin Wen (Drexel University)

Shokouh Pourarian (Drexel University)

Dan Veronica (NIST EL)

About 82 % of electrical usage in the United States primarily arises from building consumption [1], and 

approximately 84 % of the life cycle energy use of a 

building is associated with its operation rather than material and construction costs [2]. Clearly, optimal 

operational decisions are crucial to energy efficiency 

and will become more and more important as buildings 

interact more with a smart electric grid. This adds new 

opportunities to move optimal decision making for each 

building into the realm of automated so-called cyberphysical systems (CPS) which are, in turn, governed by 

artificial intelligence. For example, information provided to the building control system by the smart grid, 

such as real-time electricity pricing, can be used to make 

decisions about whether to use the power generated by 

Figure 44. Cartoon illustrating the GGSM problem: the desire is 

to capture C02 from, for example, power plant smoke stacks and 

store it (or transport it).

Figure 45. Laser sources and reflectors are used to model the size, 

shape and location of a plume.
60 NIST Applied and Computational Mathematics Division

solar panels in the building itself or sell to a utility. Engineering development of the algorithms needed to 

provide this intelligence requires a robust simulation test 

bed that currently does not exist.

HVACSIM+, the current simulation test bed, was 

developed at NIST in the 1980s for the simulation of 

heating, ventilating, and air conditioning (HVAC) systems [3]. A specialized solver was originally developed 

for HVACSIM+ but recently the character of the nonlinear systems encountered has changed dramatically. 

Simulating energy usage in buildings today requires 

nonlinear models containing far more zones (or computational blocks) than previously, and the types of 

simulation scenarios have become more complicated. 

An example of this can be illustrated in a “fan-coil”

unit (FCU), a simple but economically important structure appearing in commercial, institutional and 

multifamily residential buildings. In Figure 46, a vertical 

floor-mounted four-pipe hydronic system including 

three parallel fans run by two electric motors with three 

 

18 http://buildingsdatabook.eren.doe.gov/TableView.aspx?table=6.1.1

speeds would be used to modulate the amount of ventilation supplied by way of a motorized damper in the 

outside air connection at the back of the unit. If one were 

to simulate this scenario, variables would be typically 

grouped into blocks, control logic, actuators, air flow, 

thermal flow and a sensor block variable. These blocks 

are combined into a resulting nonlinear system which is 

solved at every time step and then matched with two exterior building zones. For this example, east and south 

facing zones are selected on a summer day. The interior 

zones can be thought of as rooms in a building, while the 

exterior zones as the region adjacent to a building. 

In summer the outdoor air damper is fully closed 

and the fan speed is normally adjusted at high. When the 

FCU is operating properly, the controller compares 

room temperature to the cooling set-point (74F or 

23.33C) and heating set-point (70F or 21.11 C). If the 

actual room temperature is greater than (cooling setpoint −1F (0.56 C)), the FCU is in cooling mode and if 

it is less than (heating set-point +1F (0.56 C)), the FCU 

is in heating mode. A dedicated proportional integral derivative (PID) loop is enabled for each mode to control 

the cooling or heating valve position. A PID loop is a 

means of regulating a process quantity (room temperature) by compensating it with closed-loop feedback of 

its error (difference between the room temperature and 

set-point), with the compensation amount computed using three gain coefficients.

It is interesting to note that even for this simple example there is no agreement between optimization 

methods (see Figure 47) and, perhaps more importantly, 

the currently employed method fails to converge at approximately t = 900. 

Current research includes investigating the reformulation of the optimization problems and 

sophisticated, specialized nonlinear solution techniques. 

If CPS are to succeed at building a strong connection 

between the physical and computational worlds then a 

robust and dependable way to simulate, for example, 

scenarios like FCUs must be developed. 

[1] DOE Buildings Energy Data Book18, 12/6/2013.

[2] World Business Council Energy Efficient Buildings 

(EEB) Report19, p. 22.

[3] D. Clark, HVACSIM+ Building Systems and Equipment 

Simulation Program Reference Manual, NBSIR 84-2996, 

National Bureau of Standards, 1984.

19 http://www.c2es.org/docUploads/EEBSummaryReportFINAL.pdf

Figure 46. Fan Coil Unit (FCU) geometry.

Figure 47. Obvious inconsistency in numerical behavior of nonlinear solvers and failure to converge of the currently employed 

method. 
Summary of Activities for Fiscal Year 2014 61

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.

Computing Properties of Materials 

with Complex 3D Microstructures

Stephen Langer

Gunay Dogan (Theiss Research)

Yannick Congo (ISIMA)

Andrew Reid (NIST MML)

See page 18.

Rheology of Dense Suspensions

William George

Steven Satterfield

Marc Olano

Judith Terrill

Nicos Martys (NIST EL)

Clarissa Ferraris (NIST EL)

Edward Garboczi (NIST MML)

Pascal Hébraud (CNRD/ESPCI, France)

See page 34.

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 

NIST’s CNST, MML, and PML, to improve the state-ofthe-art in micromagnetic modeling.

Michael Donahue and Donald Porter in ACMD have 

developed a widely used public domain computer code for 

doing computational micromagnetics, the Object-Oriented

Micromagnetic Modeling Framework (OOMMF). 

OOMMF serves as an open, 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 2014 alone, OOMMF software was downloaded more 

than 17,000 times, and use of OOMMF was acknowledged 

in more than 160 peer-reviewed journal articles. OOMMF 

has become an invaluable tool in the magnetics research 

community.

Key developments over the last year include:

 A new implementation for computing the cell-to-cell 

demagnetization tensor values that produces fourth 

order accuracy with respect to cell edge length. [1-2]

 Significant improvements to the convergence speed 

in the conjugate-gradient energy minimization code.

 An updated and improved set of online instructions 

for producing high-resolution visualizations of 

evolving magnetization patterns computed with 

OOMMF, with an extended example [3]. 

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 [4], addressing the proper calculation of the spin 

torque transfer effect was published [5] in September, 
62 NIST Applied and Computational Mathematics Division

2014. New solutions to standard problem 4 were also published [6]. 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 [7]. Collaboration 

with the University of Maryland has demonstrated nanoscale control over magnetic anisotropy in a trans-critical 

Permalloy thin film via strain-mediated coupling to ferroelectric domains in BaTiO3, a degree of control helpful in 

the aim to make compact and efficient memory devices. A 

new contributed OOMMF extension from Laboratoire de 

Physique des Solides (Universite Paris Sud) [9] adds calculation of the Dzyaloshinskii-Moriya interaction (DMI) 

to OOMMF simulations, enabling the study of skyrmions,

a subject of widespread current interest. The availability 

of the OOMMF source played a key role in a new understanding of the effect of boundary conditions on the DMI.

The ACMD micromagnetic project produced two conference presentations [1, 2], and two manuscripts 

submitted for publication [7, 8] this past year.

[1] M. J. Donahue, “A fourth order Demagnetization Tensor 

for Rectangular Prisms,” 58th Annual Magnetism and 

Magnetic Materials, Denver, CO, November 6, 2013.

[2] M. J. Donahue, “Implementation of a Localized Fourth 

Order Demagnetization Tensor,” 59th Annual Magnetism 

and Magnetic Materials, Honolulu, HI, November 5, 

2014.

[3] http://math.nist.gov/oommf/movies/oommfmovies.html

[4] M. Najafi, et al., Proposal for a Standard Problem for Micromagnetic Simulations including Spin-transfer Torque, 

Journal of Applied Physics 105 (2009) 113914-113921.

[5] http://www.ctcms.nist.gov/~rdm/std5/spec5.xhtml

[6] http://www.ctcms.nist.gov/~rdm/std4/spec4.html

[7] 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, in review.

[8] 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 Trans-critical Permalloy 

Thin Films using Ferroelectric BaTiO3 Domains, Applied 

Physics Letters 105 (2014) 212905.

[9] https://www.lps.u-psud.fr/spip.php?article2252

Shear Band Formation in Bulk 

Metallic Glasses

Timothy J. Burns

Vis Madhavan (Wichita State University)

Jue Chen (University of California)

Ryan Goh (University of Minnesota Twin Cities)

Emily McHenry (Louisiana State University)

Diego Torrejon (George Mason University)

Xin Yang (Simon Fraser University)

About thirty years ago, the problem of the localization 

of rapid plastic deformation of a number of polycrystalline metals into shear bands began to receive 

considerable attention, mainly due to its connection with 

military applications, such as armor penetration. However, the phenomenon had been observed much earlier 

in metal machining operations. At faster cutting speeds 

and larger depths of cut, the strips of work material removed by machining, called chips, were often observed 

to exhibit considerable structure, as a bifurcation took 

place in the material flow, from continuous, or fairly 

smooth chips, to serrated, or shear localized chips. The 

generally accepted explanation for the onset of this shear 

localization in polycrystalline metals is that the tendency 

of the material to work-harden with increasing plastic 

deformation is overcome by a competing tendency of 

the material to soften, due to “adiabatic” heat production 

caused by the rapid shearing of the material. Sometimes 

shear localized chips are advantageous, because they 

tend to break easily, thus simplifying chip removal. In 

other cases, localized chips degrade the quality of the 

finished surface, and they can cause tool damage. For all 

of these reasons, the localization of shear during highspeed machining of polycrystalline metallic alloys continues to be a subject of active research. 

 Recently, there has been a growing interest in the 

manufacture by machining of components made from 

amorphous metallic alloys, which are also called bulk 

Figure 48. Shear localized chips.
Summary of Activities for Fiscal Year 2014 63

metallic glasses (BMGs). These materials differ from 

common polycrystalline metallic alloys, because their 

atoms do not assemble on a crystalline lattice, and as a 

result, they have unique physical and chemical properties. See Figure 48. These materials have great 

technological potential, due to their superior mechanical 

behavior. These include a large elastic limit, very high 

strength and hardness, and resistance to corrosion and 

wear. To realize this potential, it is essential to overcome 

the severe ductility limitations of BMGs, which are 

caused by the formation of shear bands. 

A number of theoretical studies have argued that 

this strain localization is controlled not by rapid heating, 

but rather by a change in the concentration of free volume in the material. This year, analysis of a model of the 

stability of a geometrically simple shearing deformation 

in a BMG was extended to include an inelastic dilatational strain resulting from changes in the free volume. 

The work supports the free volume concentration hypothesis. 

This project was initiated at the request of Vis 

Madhavan, formerly of the NIST Engineering Laboratory, and currently at Wichita State University, and it has 

been assisted by numerical and analytical work of Jue

Chen, Ryan Goh, Emily McHenry, Diego Torrejon, and 

Xin Yang, who were graduate student participants at an 

Institute for Mathematics and Its Applications workshop 

on Mathematical Modeling in Industry in August, 2013. 

A paper on this work is in preparation.

Modeling of Shear Banding in 

Polymer Solutions

Geoffrey McFadden

Michael Cromer

Complex fluids such as polymers and multicomponent 

solutions often display a complicated relationship between the local stress field and the state of strain in the 

liquid. These fluids typically involve a microstructure 

requiring detailed modeling combined with careful and 

precise analytic and numerical techniques. The fluids of 

interest include polymer solutions, surfactants (wormlike micelles), and colloids, each of which have a 

plethora of industrial applications, such as inks, in 

homecare products, enhanced oil recovery, and other 

materials science applications. 

Simple Newtonian fluids usually exhibit a linear relation between the stress field and the strain rate in a 

flowing liquid. A simple example is the shear flow that 

is established between two parallel plates separated by a 

gap h. One plate is stationary, say in the plane y = 0, and 

the other, in the plane y = h, translates steadily in the x

direction with a velocity V. The resulting flow field has 

a linear shear profile with the local velocity u(y) = V y/h

in the x direction. On the other hand, the response of a 

complex fluid in a similar geometry can be more complex, with significant deviations from the linear shear 

profile exhibited by a Newtonian fluid. For example, under some circumstances the flow may exhibit shear 

bands, where the flow has a piecewise linear profile with 

one or more narrow transition layers separating regions 

of uniform shear. An example is shown in Figure 49, 

where the flow is based on a non-Newtonian fluid model 

of a polymer solution [1].

Figure 49. Example of shear banding in a non-Newtonian fluid. 

The black curve shows the horizontal velocity u(y) versus height y 

for a Newtonian fluid flowing between parallel plates, which a characteristic linear profile. The red curve shows the flow profile for a 

non-Newtonian fluid that exhibits shear banding, with a thin transition layer near y = 6.5 that separates high shear and low shear 

regions of flow. Here h = 10 and V = 70.

Figure 50. Bifurcation diagram showing existence of solutions with 

multiple bands. Here the amplitude of the solution shown on the ordinate is a measure of the deviation of the flow magnitude from the 

simple linear profile, and the abscissa is the pulling speed V of the 

upper of two parallel plates. The red curve shows a hysteretic solution with a single interface, which is the first banded solution to 

bifurcate with increasing pulling speed. The blue, green, and magenta curves show solutions with two, three, and four interfaces.
64 NIST Applied and Computational Mathematics Division

An interesting feature of this model is that it supports shear banding for non-Newtonian fluids that 

possess a monotonic constitutive curve that relates shear 

and strain rate. The critical feature of the model is the 

coupling of the polymer stress to the concentration profile, with shear banding associated with inhomogeneous 

concentration profiles of the polymer in solution. Numerical simulations of the nonlinear governing 

equations using spectral techniques that allow accurate 

resolution of the interfacial regions have demonstrated 

flows with multiply banded flows, with additional bands 

occurring with increasing pulling velocities V [1]. In the 

past year complementary steady-state computations 

based on quasi-Newton methods with continuation techniques are able to track these transitions in bifurcation 

diagrams such as Figure 50. This approach allows the 

computation of both stable and unstable solutions, 

providing a detailed description of the hysteresis between the unbanded and banded flow states that is 

observed under some conditions. Additional research is 

addressing the detailed flow in the transition region between bands as a problem in matched asymptotic 

expansions in a thin interface limit; here the interface 

thickness is controlled by the “correlation length’’ of the 

polymer solution.

This project is continuing in several directions, including the consideration of curved geometries such as 

the Taylor-Couette flow between concentric rotating 

cylinders. M. Cromer recently completed an NRC Postdoctoral Associateship in ACMD, and is currently on the 

faculty of the School of Mathematical Sciences at the 

Rochester Institute of Technology in New York.

[1] M. Cromer, M. Villet, G. Fredrickson and L.G. Leal, A 

Study of Shear Banding in Polymer Solutions, Physics of 

Fluids 26 (2014) 063101.

Estimation of Shear Stress in 

Machining 

Timothy J. Burns 

Bert W. Rust

After decades 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 open problem. 

This limits the ability of manufacturers to predict optimal cutting conditions for a given process. A major 

reason for this limitation is that current materials testing 

facilities, such as a Kolsky bar laboratory, cannot measure the stress vs. strain response of materials like 

titanium and iron alloys under the extreme conditions of 

rapid heating that are present in typical high-speed metal 

machining operations. For example, in a fairly routine 

cutting process on a modern machining center, a heating 

rate on the order of one million degrees Celsius per second is not uncommon for carbon steels.

We are investigating a new approach to the problem

of estimating flow stress in machining. The recent invention by Menon and Madhavan [1] of a cutting tool 

that is transparent in infrared frequencies makes it possible to obtain good in-situ temperature measurements 

along the chip-tool interface during a steady-state machining operation. This enables an estimate to be made 

of the shear stress distribution in the work material along 

the face of the tool under actual machining conditions,

by means of an inverse method [2]. By solving a convection-diffusion problem that models the flux of heat 

into the chip and the tool during a cutting process, the 

temperature distribution along the tool face can be 

shown to satisfy the dimensionless equation

Θ(X) =

ν

√π

∫

Σ(U)

√(X − U)

dU (1)

X

0

Here, Θ is the normalized temperature, Σ is the normalized flow stress, X [0,1] is the distance along the 

contact surface on the face of the tool, measured from 

the tooltip, and ν is a parameter that is O(1).

Viewed as an inverse problem, Eq. 1 is a Volterra 

integral equation of the first kind, Abel’s equation, for 

the determination of Σ(X) on [0, 1], given Θ(X). Under 

mild regularity assumptions on the function Θ(X), the 

solution to Eq. 1 is well known,

ν

√π

Σ(X) =

1

π

d

dX ∫

Θ(U)

√X −U

dU (2)

X

0

=

1

π

{

Θ(0)

√X

+ ∫

Θ

′

(U)

√X − U

dU

X

0

}. (3)

It is clear from Eq. 3 that, for Σ(X) to be continuous at 

X=0, the nondimensionalized temperature must satisfy 

Θ(0) = 0. A major difficulty in applying this inverse 

method is that the temperature data are experimentally 

determined at a finite number of points, so that they are 

inexact, and the formulas (2) and (3) involve numerical 

differentiation of these data, which is an ill-posed problem. If the data are equally spaced with increment h and 

2σ error bars bounded by δ, then using the midpoint 

product integration method, it can be shown that the error in the computed stress will be of order δ/h

1/2 [3].

When δ is significant, some kind of regularization 

method is required in order to separate signal from noise 

in the temperature data. We are investigating the use of 

Rust’s truncated singular components method (TSCM) 

[4] to invert the Abel equation and obtain an estimate of 

the stress. This method involves solving the linear system of equations which arises from the discretized Abel 

equation by truncating the singular vector expansion rather than the singular value distribution of the

approximate linear system. The method is a variant of 

principal components regression which does not use the 
Summary of Activities for Fiscal Year 2014 65

singular values to choose the principal components. It 

produces residuals which are closer to uncorrelated 

white noise.

[1] T. Menon and V. Madhavan. High Accuracy Full-field 

Infrared Thermography of the Chip-tool Interface 

through Transparent Cutting Tools while Machining Ti6Al-4V, in review.

[2] T. J. Burns, S. P. Mates, R. L. Rhorer, E. P. Whitenton

and D. Basak, Inverse Method for Estimating Shear 

Stress in Machining, in review.

[3] P. Linz, Analytical and Numerical Methods for Volterra 

Integral Equations, SIAM, Philadelphia, 1985.

[4] B. W. Rust, Truncating the Singular Value Decomposition for Ill-Posed Problems, NISTIR 6131, July 1998.

Uncertainty Quantification and 

Molecular Dynamics Simulations of 

Aerospace Polymers

Andrew Dienstfrey

Paul Patrone (University of Minnesota)

With the increasing power and availability of scientific 

computing, the composites industry is heavily investing 

in molecular dynamics (MD) as a cost-effective tool for 

identifying next generation, high-performance materials 

[1, 3]. For example, in aerospace applications MD is being considered to search the combinatorially-large 

polymer design space for systems whose mechanical 

properties warrant further experimental study. While 

this strategy holds promise, the high-throughput demands of industry can extend simulations toward the 

limits of their validity. Thus, a key task is to assess confidence in such computations, rendering their 

predictions more informative for decision making in the 

materials development cycle. The growing field of uncertainty quantification (UQ) provides a useful 

foundation from which to develop and analyze such 

techniques [4]. 

Simulation-based prediction of the glass transition 

temperature Tg is an especially interesting problem 

against which to investigate this development. In composites Tg characterizes the boundary between elastic 

and fluid-like behavior of molecular constituents. Macroscopically, this transition determines the ability of a 

structural component, for example an airplane wing, to 

remain rigid at high temperatures. While Tg is both a natural and critical property characterizing polymer 

systems, identifying Tg from MD simulations is a challenging task. The dynamic processes associated with 

glass formation are inherently non-equilibrium. Moreover, the underlying molecular structure of cross-linked

polymers is a realization of a large random network. 

Thus, in using atomistic simulations to predict Tg, it is 

desirable to simulate large systems over long times to 

sufficiently average cross-linking statistics and collective dynamics. Given that MD falls short of these scales 

by several orders of magnitude, the question naturally 

arises as to how trustworthy are estimates of Tg obtained

from molecular dynamics simulations [3].

In 2014 we developed tools to address this question. 

We simulated a large number of epoxy-amine systems 

built-up of from 2000 to 16000 atoms; see Figure 51. 

The candidate systems were cross-reacted (in silico), 

and then cooled from 800 K to 100 K at a constant rate. 

Density-vs-temperature curves of glass-forming polymers exhibit asymptotic, high- and low- temperature 

regimes in which density, ρ(T), is effectively linear. For 

both experimental and virtual measurement contexts, Tg

is defined as the boundary temperature between these 

two. Ambiguity in identifying such a transition is one 

source of uncertainty in computational estimate of Tg;

see Figure 52. To reduce this ambiguity, we propose to 

model curves ρ(T) data as a hyperbola with parameters

defined by a nonlinear optimization. We implemented 

two methods for propagating the uncertainty in this fitting process and showed that they result in 

commensurate estimates of the uncertainty of Tg for any 

given realization of a polymer system. However, as we 

have shown, this analysis reflects only part of the total 

uncertainty associated with MD-derived measurement

of Tg. Additional sources of uncertainty arise from finite 

exploration of the energy landscape and limited sampling of cross-linking configurations. This year we 

began to account for these uncertainty sources, modeling so-called “dark-uncertainty” using a mixed-effect 

statistical analysis motivated by key-comparison analysis in metrology. A paper is in progress. We hope to 

continue and extend this work with industrial stakeholders in the coming year.

In addition to this MD-polymers application, in 

2014 we also continued outreach into the broader computational material science community as part of the 

Materials Genome Initiative (MGI). MGI is a multiFigure 51. Unit cell showing cross-linked polymer system containing 2000 atoms. Molecular dynamics evolves atoms by Newtonian 

dynamics using potential model to compute inter-atomic forces.
66 NIST Applied and Computational Mathematics Division

agency initiative launched by the White House in June 

2011. The purpose of MGI is to promote creation of 

novel materials for use by industry with significant reductions in time and cost. Widespread availability of 

materials data and increased use of models and simulations are critical engines to drive this progress. In 

December 2013 NIST co-hosted a working conference

at the Institute for Mathematics and its Applications at 

the University of Minnesota. The goal of that meeting 

was to bring together stakeholders from industry, academia, and government labs to explore the overlaps

between uncertainty analysis, computation, and materials science. Results were described in a paper coauthored by a cross-cut of participants that appeared in 

June 2014 [2]. A key-finding emerging from workshop 

discussion sessions was the need to create working examples of uncertainty quantification analysis as applied 

to computational material science to serve as bridges between the two communities. Toward this goal we are 

currently organizing a follow-up working conference to 

be held at Purdue University, University in July of 2015. 

We look forward to reporting on this effort next year.

[1] B. Cowles, D. Backman and R. Dutton. Verification and 

Validation of ICME Methods and Models for Aerospace 

Applications, Integrating Materials and Manufacturing 

Innovation 1:1 (2012).

[2] A. Dienstfrey, F. R. Phelan, S. Christensen, A. Strachan, 

F. Santosa and R. Boisvert, Uncertainty Quantification in 

Materials Modeling. JOM 66:7 (July 2014), 1342-1344.

[3] C. Li and A. Strachan, Molecular Scale Simulations on 

Thermoset Polymers: A Review, Journal of Polymer Science Part B: Polymer Physics 53:2 (2015), 103-122.

[4] J. H. Panchal, S. R. Kalindini, and D. L. McDowell, Key 

Computational Modeling Issues in Integrated Computational Materials Engineering, Computer-Aided Design

45:1 (2013), 4-25.

Stability of a Solid-Liquid Interface 

during Solidification

Geoffrey McFadden

Sam Coriell (NIST MML)

Robert Sekerka (Carnegie Mellon University)

A fundamental problem in the material processing of 

multicomponent alloys is to determine the stability of 

the crystal-melt interface that separates the solid and liquid phases during growth from the melt. Instability of 

the interface generally leads to undesirable inhomogeneities in the solute distribution in the crystal, which can 

cause significant degradation of the electrical and mechanical properties of the product. The original 

treatment was worked out by W. W. Mullins and R. F. 

Sekerka in 1964 [1], and now goes under the name of

morphological stability theory. The 1964 paper has over 

2500 citations, and the work has been reviewed numerous times, including a chapter in the 1993 publication of 

the Handbook of Crystal Growth by S. Coriell and G. 

McFadden [2]. An updated article that includes recent 

work performed subsequent to that review was recently 

completed and has now appeared in the second edition 

of that handbook [3].

[1] W. W. Mullins and R. F. Sekerka, Stability of a Planar 

Interface during Solidification of a Dilute Binary Alloy, 

Journal of Applied Physics 35 (1964) 444-451.

[2] S. R. Coriell and G. B. McFadden, Morphological Stability, in Handbook of Crystal Growth, Vol. 1B, (D. T. J. 

Hurle, ed.), Elsevier, Amsterdam, 1993, 785-857.

[3] R. F. Sekerka, S. R. Coriell and G. B. McFadden, Morphological Stability, in Handbook of Crystal Growth, 

Vol. I, 2nd Edition, (T. Nishinaga, ed.), Elsevier, Amsterdam, 2015, 595-630.

Surface-Active Diffuse Interface 

Model

Sean Colbert-Kelly

Geoffrey McFadden

Frederick R. Phelan, Jr. (NIST MML)

Surfactants are chemical compounds that lower interfacial tension between two liquids or a liquid and a solid. 

Surfactants have important applications in detergents, 

droplet break-up, and reducing the risk from bubbles 

formed in blood due to rapid decompression [2, 3]. This 

research project studies the transition that occurs between two immiscible fluids with surfactant at the 

interface between the two fluids. 

The mixing properties of the two fluids affect the 

interface shape dynamics. Because surfactants lower interfacial tension there are gradients in the surfactant 

Figure 52. Density versus temperature plot as obtained by simulation are shown as blue dots. Asymptotic linear trends can be 

observed at low and high temperatures. Tg is defined as the intersection of these two “best-fit” lines. Subjective determination of the 

high-temperature asymptotic regime results in variation of Tg .
Summary of Activities for Fiscal Year 2014 67

concentration on the drop surface under flow, giving rise 

to Marangoni forces that alter drop shape, breakup and 

coalescence dynamics, as well as flow induced migration [1]. Surfactants migrate to the fluid interface in a 

binary mixture due to the amphiphilic nature of these 

molecules [2]. The presence of the surfactant produces 

dramatic changes in the interfacial properties of the fluid 

mixture, and therefore greatly alters the stability, equilibrium properties, and the droplet dynamics of the 

mixture. These dynamics govern the long time stability 

of emulsions. Current models do not accurately model 

the dramatic effects of surfactants on emulsion properties and dynamics.

Discontinuities in fluid properties tend to complicate flow computations along the interface between two 

liquids or a liquid and a solid. Properties such as surface 

energy and surface viscosity also complicate such calculations. A diffuse interface model (DIM) can be useful 

in investigating such interfacial dynamics. 

From studying previous work, this project intends 

to develop and analyze a description of the mixture of 

two immiscible fluids with surfactants where mixing can 

occur near the interface, while incorporating interfacial 

properties that many DIMs tend to ignore. Currently, it 

is assumed that the two liquids are considered Newtonian and incompressible, where in the interfacial region 

this assumption may not hold. In addition, this project 

will study the limiting problem of the diffuse interface 

model, to determine if a sharp interface model is recovered in letting the interfacial region get arbitrarily thin. 

It will also be of benefit to study the deformation of the 

droplet, and determine if the droplet will remain spherical in shape. 

Represent the binary fluid by a phase field variable 

c, with c ε [-1,1], c = 1 represents one fluid and c = -1 

represents the other fluid. Represent the surfactant by 

the variable ψ, with ψ ε [0,1], and the fluid velocity u. 

Then the governing equations for the binary fluid and 

surfactant are

∂c

∂t + ∇ ∙ (cu) = ∇ ∙ (Dc∇μc

)

∂ψ

∂t + ∇ ∙ (ψu) = ∇ ∙ (Dψ∇μψ).

Dα is the mobility constant and μα is the chemical potential for that particular variable. The continuity equations 

are coupled with the following Navier-Stokes equations

∇ ∙ u = 0

ρ (

∂u

∂t + u ∙ ∇u) = −∇p +∇ ∙ η(∇u +(∇u)

T

)

+μc∇c + μψ∇ψ.

Initial analysis assumes that Dα, μα, and η are constant. Incorporating a non-constant interfacial viscosity, 

η(x), is the next step to this project. Reference [4] incorporates a mixing rule in the binary case (no surfactant in 

the system) to incorporate the effect of interfacial viscosity describe the viscosity change in the interfacial

layer due to the decreased entanglement of polymers. In 

the case of surfactant in the system, no method has been 

considered on incorporating interfacial viscosity. However, it is proposed that interfacial viscosity should be 

dependent on the surfactant ψ.

[1] J. T. Schwalbe, F. R. Phelan, Jr., P. M. Vlahovska, and S. 

D. Hudson, Interfacial Effects on Droplet Dynamics in 

Poiseuille Flow, Soft Matter 7 (2011), 7797–7804.

[2] S. Engblom, M. Do-Quang, G. Amberg, and A.-K. Tornberg, On Diffuse Interface Modeling and Simulation of 

Surfactants in Two-phase Fluid Flow, Communications 

in Computational Physics 14:4 (2013), 879-915.

[3] C.-H. Teng, I.-L. Chern, and M.-C. Lai, Simulating Binary Fluid-Surfactant Dynamics By a Phase Field Model,

Discrete and Continuous Dynamical Systems Series B

17:4 (2012), 1289–1307.

[4] W. Yu and C. Zhou, The Effect of Interfacial Viscosity 

on the Droplet Dynamics under Flow Field, Journal of 

Polymer Science Part B: Polymer Physics 46:14 (2008), 

1505-1514.

Spectral-Galerkin Scheme to Study 

Ferroelectric Liquid Crystal

Properties

Sean Colbert-Kelly

Geoffrey McFadden

Daniel Phillips (Purdue University)

Jie Shen (Purdue University)

This project considers the effect of introducing defects 

into a ferroelectric liquid crystal thin film. If a small foreign particle is introduced into a thin chiral smectic c 

(SmC*) film, a disk-like island will form around the defect several layers thicker than the surrounding thin film

[1]. On the island’s boundary, the director field u is tangential counterclockwise and is initially tangential in the 

interior of the disk, making a degree 1 vector field. 

However, increase in the island's size or external forces 

can cause distinct textural transformations in the director 

field. The pattern can remain unchanged or transform to 

what is called a simple spiral, tangential counterclockwise on the boundary and approximately radial at the 

smoke particle boundary [1].

The elastic energy of this system in the island can 

be described by

Eε

(u) =

1

2

∫ ks

(∇ ∙ u)

2 + kb

B1

(∇ × u)

2

+

1

2ε

2

(1 −|u|

2

)

2 dx,
68 NIST Applied and Computational Mathematics Division

where ks, kb are the splay and bend constants for the liquid crystal, and ε > 0 is the radius of the defect core; in 

this model u is not restricted to having unit length. The 

director field u is given boundary conditions, i.e., u = g

where |u| = 1 and g had degree d > 0. For each ε, a minimizing vector field uε exists as ε ⟶ 0, uε ⟶ u∗. The 

asymptotic field u∗ has degree d = 1 singularities and, 

near a singularity, a, u∗ behaves locally as

u∗ = αa

x −a

|x −a|

where αa = ±1 for ks < kb and αa = ±i for ks > kb

[2].

The purpose of this project is to develop a spectralGalerkin numerical method for the Euler-Lagrange 

equations for Eε when ε is small, so as to capture the experimental observations and analytical results described 

above. Thiis will enable us to view the nature of the 

defects computationally and observe results not currently proven analytically. Many numerical methods 

deal with the simpler case ks = kb, resulting in a vector 

version of the Allen-Cahn equation. Our method will 

also simulate the case ks ≠ kb [3, 4]. We develop a gradient flow stabilized scheme for the Euler-Lagrange 

equations and let the solutions stabilize to an equilibrium state. We discretize the Euler-Lagrange equation 

via a first order semi-implicit stabilized scheme. The 

equation is then converted into a polar geometry representation. With this representation, we can approximate 

the solution with a Fourier expansion in the angle variable using an FFT and then approximate the Fourier 

coefficients using Chebyshev polynomials in the radius 

variable. This scheme has been shown to be unconditionally stable with error estimates on the order of 

exp(T/ε

2

) . We tested the scheme with boundary conditions of the form g = exp(diθ), for d any positive integer.

Figure 53 plots the minimum vector field orientation uε for the case d = 1. The top figure is the stable 

solution for the energy with values ks = 0.5, kb = 1.5 and 

g = exp[i(θ-π/2)], while the bottom figure is the stable 

solution for the energy with values ks = 1.5, kb = 0.5 and 

g = exp[iθ]. We see that in the case ks < kb the vector 

field is nearly radial near the origin. When ks < kb, the 

vector field is nearly tangential near the origin. This follows what was shown analytically. The plot in the case 

ks < kb follows what was seen experimentally as well. In 

the case ks < kb with the vector field tangential to the 

boundary, either clockwise or counterclockwise, the stable vector field is a simple spiral. 

Lee, Konovalov, and Meyer [1] note that the size of 

the island also affects the transformation of the vector 

field: if the island radius is small the pure bend patterns 

rarely transform to a simple spiral. Related computational results are shown in Figure 54. The equilibrium 

configuration of the degree one solutions in Figure 53

can be represented in the form

u(r, θ) = ν(r)r̂(θ) +w(r)θ̂(θ) = [ν(r)+ iw(r)]e

iθ

where the scalar functions ν(r) and w(r) and represent 

the splay and bend components of u in the radial direction r̂(θ) and angular direction θ̂(θ) respectively. The 

left plot is a plot of the maximum value of the bend component w as a function of ε, which describes a 

bifurcation from the splay solution, w = 0, at εb ≈ 0.244.

The right plot is the energy of the spiral solution (black 

Figure 53. Stable vector fields to the elastic energy.

Figure 54. Behavior of the steady-state spiral solution as a function 

of ε for ks = 1.5 and kb = 0.5.
Summary of Activities for Fiscal Year 2014 69

curve) and the splay solution (red curve) versus ε, which 

shows that the spiral solution is stable for ε < εb. In this 

study we have also performed a number of numerical 

simulations of both the lowest energy solution and 

higher energy solutions with a variety of boundary conditions of various degrees d; the higher energy solutions 

are generally degenerate, with several possible locations 

of the defects that depend on the values of ks and kb. 

[1] J.-B. Lee, D. Konovalov and R. B. Meyer, Textural 

Transformations in Islands on Free Standing Smectic-C* 

Liquid Crystal Films, Physical Review E 73 (2006), 

051705.

[2] S. Colbert-Kelly and D. Phillips, Analysis of a GinzburgLandau Type Energy Model for Smectic C* Liquid Crystals with Defects, Annales de l'Institut Henri Poincare (C) 

Non Linear Analysis 30:6 (2013), 1009-1026.

[3] J. Shen, Efficient Spectral-Galerkin Methods III: Polar 

and Cylindrical Geometries, SIAM Journal on Scientific 

Computing 18:6 (1997), 1583-1604.

[4] J. Shen and X. Yang, Numerical Approximations of Allen-Cahn and Cahn-Hilliard Equations, Discrete and 

Continuous Dynamical Systems. Series A 28:4 (2010), 

1669-1691.
Summary of Activities for Fiscal Year 2014 70

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 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.

High Precision Calculations of 

Fundamental Properties of FewElectron Atomic Systems

James Sims

Stanley Hagstrom (Indiana University)

See page 31.

Rheology of Dense Suspensions

William George

Steven Satterfield

Marc Olano

Judith Terrill

Nicos Martys (NIST EL)

Clarissa Ferraris (NIST EL)

Edward Garboczi (NIST MML)

Pascal Hébraud (CNRD/ESPCI, France)

See page 34.

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)

Research and development of nanotechnology, with applications ranging from smart materials to quantum 

computation to biolabs on a chip, is an important national priority. Semiconductor nanoparticles, also 

known as nanocrystals and quantum dots (QDs), are one 

of the most intensely studied nanoscale systems. Nanoparticles are typically 1 nm to 10 nm in size, with a 

thousand to a million atoms. Precise control of particle 

size, shape and composition allows one to tailor charge 

distributions and control quantum effects to tailor properties completely different from the bulk and from small 

clusters. As a result of enhanced quantum confinement 

effects, nanoparticles act as artificial, man-made atoms 

with discrete electronic spectra that can be exploited as 

light sources for novel enhanced lasers, discrete components in nanoelectronics, qubits for quantum computers, 

and enhanced ultrastable fluorescent labels for biosensors to detect, e.g., cancers, malaria or other pathogens, 

and to do cell biology. 

We are working with the NIST PML to develop 

computationally efficient large scale simulations of such 

nanostructures, as well as to develop immersive visualization techniques and tools to enable analysis of highly 

complex computational results of this type. The electrical and optical properties of semiconductor nanocrystals

and quantum dots are studied. In the most complex 

structures, this entails modeling structures with on the 

order of a million atoms. Highly parallel computational 

and visualization platforms are critical for obtaining the 

computational speeds necessary for systematic, comprehensive studies.

Parallel Computing. This year our work has focused on 

modulating and controlling the optical properties of selfassembled quantum dots using both electric and magnetic fields. The electric field work culminated in a 

paper in Physical Review B [1]. Calculations were carried out on NIST’s 7892 processor Linux cluster. 

In addition to the electric field work, we have modified the code to handle the imaginary parameters due to 

the magnetic field (electric field parameters are real) and 

there are now data input files for both electric fields and 
Summary of Activities for Fiscal Year 2014 71

magnetic fields. New computational studies incorporating the effect of magnetic fields continue to be done. In 

addition, code has been written which identifies the 

wave function states of maximum and minimum spin, 

which would form the qubit for quantum computing. 

The addition of a magnetic field provides a probe to 

split excitonic states, providing a more complete spectroscopy of quantum dot optics. This allows us to isolate 

contributions from spin-orbit coupling, Zeeman and spatial motion. Magnetic field response depends sensitively 

on the QD size and shape. 

We consider pyramidal and flat QDs to identify the 

size and shape dependence of g-factors, g-factor anisotropy and electric-field tuning, diamagnetic shifts, and 

spin and level mixing as a function of magnetic field 

magnitude and orientation. 

The intrinsic spin of the electron can lead to different effects in a magnetic field depending on the QD size 

and shape, so it is necessary to see the effect of spin in 

different QD arrangements. Without visualization, it is 

difficult to understand what the spin distribution is and 

how it changes for different magnetic fields, electric 

fields or strain. This distribution is critical for understanding exchange interactions or electron/nucleus

interactions in quantum devices. These properties are intimately connected with the performance of these 

structures in quantum information processing [2, 3]. 

In the future, the codes will be revised to incorporate deterministically placed dopants (phosphorous) in 

Si to simulate Si-based dopant devices that are only a 

few atoms wide. This will require re-evaluation of the 

parallelization techniques in use. 

Visualization. As part of a continuing NIST grant 

award, Jian Chen developed a novel visual encoding 

method to visualize the simulation results. The new 

Figure 55. Visual encodings of vector field data: (a) the linear representation fails by only showing a small range of the data; (b) a logarithmic 

encoding successfully shows the data, but requires more mental calculation to understand the data; (c) attaches text labels to each data point, 

which, while highly accurate, obscures the vector field; (d) visualizes the entire range of the data while also allowing easier fine-grain understanding of the vector data.
72 NIST Applied and Computational Mathematics Division

method was necessary because the vector field data has 

a very large range of magnitude which causes other visual encodings to fail. In Figure 55(a), the linear 

representation fails by only showing a small range of the 

data. The small magnitude data disappears and the large 

magnitude data overwhelms the rest of the data. In Figure 55(b), a logarithmic encoding successfully shows 

the data, but requires more mental calculation to understand the data. Figure 55(c) attaches text labels to each 

data point, which, while highly accurate, obscures the 

vector field. Finally, the new encoding in Figure 55(d) 

visualizes the entire range of the data while also allowing easier fine-grain understanding of the vector data. 

The new method splits the direction and magnitude of 

each vector into two pieces and encodes the two pieces 

separately to enhance comprehension. The new encoding was developed as part of a larger visualization tool 

that runs on the desktop. It was created in close cooperation with Garnett Bryant in PML to ensure his 

requirements for data exploration were met. 

The results of this work should directly benefit Bryant and his research into quantum dots and electron spin 

distribution. Furthermore, the novel visual encoding for 

vector data has larger applicability in the field of visualization. A paper describing this new visual encoding is 

in process. A poster describing this work is under review 

at IEEE VR 2015 [4]. Also, Jian Chen will be giving an 

oral presentation at IEEE VR 2015 about her research 

lab and will be discussing this work [5]. 

Future work will include a paper on this novel encoding approach as well as a user-study to determine its 

effectiveness in the CAVE. We will also work on extending the desktop visualization tool to the CAVE. 

[1] G. W. Bryant, N. Malkova and J. Sims, Mechanism for 

Controlling the Exciton Fine Structure in Quantum Dots 

using Electric Fields: Manipulation of Exciton Orientation and Exchange Splitting at the Atomic Scale, Physical 

Review B 88 (2013),161301(R). 

[2] G. W. Bryant and J. Sims, “g-factors, Diamagnetic Shifts 

and Spin Polarization in Quantum Dots: The Role of 

Shape, Spin Mixing and Spin Texturing,” International 

Conference on Quantum Dots (QD2014), Pisa, Italy, May 

11-16, 2014. 

[3] G. W. Bryant, “Controlling Quantum Dots,” Institute 

Seminar, University Nicholas Copernicus, Torun, Poland, October 2014. (invited)

[4] 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 Environments (poster) IEEE Virtual Reality

(VR2015), March 23-27, 2015, Arles, France. 

[5] J. Chen, J. E. Terrill, H. Zhao, G. Zhang, K. Wu, A. Garbrino and Y. Zhu, Interactive Visual Computing 

Laboratory Research, Laboratory and Project Presentations Track, IEEE Virtual Reality (VR2015), March 23-

27, 2015, Arles, France.

Modeling and Visualization of 

Cement Paste Hydration and 

Microstructure Development

John Hagedorn

Steven Satterfield

Judith Terrill

Terence Griffin

Wesley Griffin

Franz Sauer (University of California at Davis)

Earl Bellinger (SUNY Oswego)

Alicia Ouyang (River Hill High School)

Romain Desaymons (ISIMA)

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

When cement powder is mixed with water, the hydration 

process that transforms the paste from a fluid suspension 

into a hardened solid involves complex chemical and 

microstructural changes. Understanding and predicting 

the rates of these changes is a longstanding goal. 

Computational modeling of the hydration of cement is 

challenging because it involves a large number of 

coupled nonlinear rate equations that must be solved in 

a highly irregular three-dimensional spatial domain. To

address these challenges we are applying a new 

computational model called HydratiCA, which has

several advantages over other models of cement 

hydration. HydratiCA uses stochastic cellular automata 

algorithms to simultaneously model reaction and 

transport phenomena in 3D. This allows us to track the 

detailed kinetics and equilibria that occur in a diverse 

range of cementious systems.

Parallelization of the model and visualization of the 

output data are important. 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. Over the 

course of the simulation time, a series of data volumes 

is produced at the time values of interest. Visualization 

of this data is valuable both for validation and for 

understanding of the results.

This year we requested and received from NSF a 

renewal of our 100,000 hour grant of computer time on 

the Texas Advanced Computing Center’s Dell 

PowerEdge C8220 Cluster with Intel Xeon Phi

coprocessors (Stampede). We extended our tool for 

analyzing the output files to study the degree of

hydration over time including the duration of the drowsy 

period, the peak rate, and the time of the peak.

Several changes were made to the model to improve 

its ability to simulate the complex dissolution, 

nucleation and growth of cementitious solids, including:
Summary of Activities for Fiscal Year 2014 73

 Development of a generalized, but empirical, rate 

law for dissolution that embraces a wide range of 

kinetic behavior, from highly nonlinear 

dependence on undersaturation to the standard rate 

law for elementary reactions. This rate law has 

been shown to more accurately capture the 

dissolution rates of C3S, the majority mineral in 

unhydrated cement powders.

 Several improvements in the algorithms for 

heterogeneous and homogeneous nucleation and 

growth, so that these processes are now more 

closely tied to classical nucleation theory and are 

able to more directly accept experimental 

parameters that can be measured in the laboratory.

These additions to the model revealed several latent 

bugs in the source code, especially when implemented 

in a parallel computing environment, that were difficult 

to pinpoint. To remedy this, we developed an interactive 

visualization and analysis environment, which ran both 

in our immersive environment and on the desktop, for 

the model output. This environment provided a variety 

of visual modes that enabled precise quantitative 

measurements. It combined 3D scientific visualization 

with information visualization using D3.js running in a 

web browser. These two visualizations used node.js to 

communicate bidirectionally thereby simplifying 

analysis. See Figure 56 and Figure 57.

The visualization and analysis tool quickly showed 

what was causing the output errors and we were able to 

correct those bugs in the source code. In the coming 

year, we will be using and extending this and other tools 

to validate the outputs of our runs to study the rate 

controlling mechanism for early-age cement hydration.

[1] J. Stoian, T. Oey, J. Huang, A. Kumar, J. W. Bullard, M. 

Balonis, S. G. Satterfield, J. E. Terrill, N. Neithalath and 

G. Sant, Prehydration of Ordinary Portland Cement and 

its Mitigation using Limestone: New Insights from 

Experiments and Simulations, in review.

[2] W. Griffin, Danny Catacora, Steven Satterfield, Jeffrey 

Bullard and J. Terrill, Incorporating D3.js Information 

Visualization into Immersive Virtual Environments, 

poster VR2015 IEEE Virtual Reality, 23-27 March 2015, 

Arles, Camargue, Provence, France.

Figure 57. 3D Heat Map and Concentration Data Visualization.

Figure 56. 2D information visualization with cross section of 3D visualization, network of chemical reactions, and activation rate histogram..
74 NIST Applied and Computational Mathematics Division

New Immersive Virtual 

Environment 

Steve Satterfield

John Hagedorn

Wesley Griffin

Terence Griffin

Judith Terrill

The High Performance Computing and Visualization 

Group (HPCVG) has operated an Immersive Virtual Environment (IVE) since 2000 in support of its mission to 

develop the infrastructure necessary for advanced visualization of scientific data, including the use of 3D 

immersive environments as a true interactive measurement laboratory. HPCVG collaborates with researchers 

across all areas of NIST to apply the IVE and virtual 

measurement techniques. 

During 2014, the IVE underwent a major upgrade, 

essentially a replacement, providing a significant improvement in visual quality. The new IVE, known as the 

CAVE, 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 which allows one of three computers to be selected as the CAVE 

host at the touch of a button. This enables 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. 

With the new installation a proactive approach to reliability was taken. Included with the hardware 

procurement, a custom software component for selfmonitoring of the hardware was specified and delivered. 

Combined with a few existing system tests it is now possible to run automated tests nightly to confirm correct 

operation of many CAVE sub-systems and components. 

While certain tests require human observation, the automated self-test software provides a high level of 

confidence for on-going system availability. The selfmonitoring software tests for: tracker producing head 

and wand data; projectors powered off when CAVE not 

in use; projectors shutter on/off operation; video switch 

operation; USB switch operation; audio switch operation; and changes in the critical /etc/X11/xorg.conf file. 

The self-monitoring software also includes tests run 

manually to check for 3D glasses synchronization or eye 

swap errors and a projector power cycle operation. 

While not specifically a test, the software includes a 

mechanism for powering off the projectors remotely. 

Equally as important to the success of the IVE is the 

software used to drive the CAVE and implement the 

specific applications. At the lowest level, the vendorsupplied OpenGL library and Linux device driver renders and displays graphics in the graphics cards 

producing images output to 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 update in real time the projected images. 

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 that the 

displayed scene graph can be modified at run-time by 

external processes (programs and scripts) communicating via a standard Linux/UNIX facility known as a 

“named pipe.” Another feature of IRIS and HEV is device independence. By isolating the display 

characteristics into specific display DSOs (distributed 

shared objects), the same HEV binary code can run on a 

full range of devices from CAVES to non-immersive 

desktop/laptop displays.

IDEA (IRIS Development Environment for Applications) is the level above IRIS. It is an HPCVG 

developed 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 focuses on one 

simple task useful for a wide variety of applications. 

Applications and demos complete the stack typically implementing an interactive visualization in a 

specific area of research. 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 

software stack. A typical scenario combines traditional 

immersive visualization with 2D analysis capability and 

bidirectional communication between the 3D and 2D 

visualizations, creating an interactive virtual laboratory 

in the CAVE. See Figure 58 for an example of a collaborative session in HPCVG CAVE. In the coming year, 

besides our visualizations, we will be designing and implementing a software testing capability. 

Figure 58. A collaborative session in the HPCVG CAVE.
Summary of Activities for Fiscal Year 2014 75

Optical Characterization of Large 

Immersive 3D Displays

Steve Satterfield

Judith E. Terrill

John Penczek (NIST PML)

Paul A. Boynton (NIST PML)

Timothy Scheitlin (NCAR)

Many things influence a visualization of a dataset. These 

include the nature of the data itself and its uncertainties, 

the visual representation space, the visualization algorithms, as well as algorithmic simplifications. Another 

factor impacting the final visualization is how accurately 

the images are rendered by the display system. We seek

to develop a deeper understanding of each part of this 

process. In the current work we are studying the impact 

of the display on stereo visualizations.

Every display technology has its own inherent performance limitations. The non-ideality of the display 

introduces constraints on what information can actually 

be observed by the viewer. By characterizing the optical 

performance of the display system, we can quantitatively determine what visual information may be 

impaired. Operators of display facilities can use these

results to evaluate how visual characteristics that are important to them are affected, understand the visual 

limitations of their system, and ultimately to drive improvements. The display performance data also informs 

scientists that create the visualization data how much of 

that data can actually be realized/observed. For example, 

the contrast ratio of an image feature can be dramatically 

degraded with the introduction of ambient lighting. 

Light contamination can be especially problematic for 

multi-wall CAVE systems, where the images from the 

adjacent screen can reduce the viewability at the region 

of interest. In addition, Figure 59 also illustrates how the 

spatial distribution of the contrast ratio on the front 

screen of a multi-wall CAVE system changes when the 

adjacent walls are turned on (right image). This report 

summarizes our activities in optically evaluating the 

viewing performance of a modern multi-wall CAVE 

system, and the impact of ambient lighting in general on 

several 3D immersive displays.

Our prior work largely focused on single-wall 3D 

immersive displays, see displays #1 and #2 in Table 2. 

The current work includes a 4-wall CAVE system that 

was recently installed at an offsite facility (display #3 in 

Table 2). The suite of tests developed for the single-wall 

displays were also applied to the 4-wall CAVE [1-4]. 

The optical characteristics measured on these systems 

included: luminance and color difference between left 

and right eye, contrast ratio between left and right eye, 

crosstalk between left and right eye, viewing direction 

dependence, head tilt dependence, luminance and color 

uniformity, shutter glasses characteristics, and 2D crosstalk and contrast mapping. Care was taken to separate 

the contribution of light scattering from the adjacent 

projection walls. The front screen of the CAVE system 

was initially optically characterized with the adjacent 

walls turned off in order to evaluate the intrinsic capabilities of the display system. These measurements 

demonstrated that the darkroom characteristics of this 

new display system (display #3) had superior luminance, color, and contrast than the older single-wall 

systems. This demonstrated the improvements in viewing performance made by industry over time, and where 

further improvements can be made.

Another important aspect investigated by this study 

was the influence of ambient lighting. In the case of the 

single-wall displays, unintended light from scattering in 

the room or overhead lighting can add background noise 

to the viewing field on the screen and degrade the quality of the image. For display #1, the display is normally 

viewed in a dark room where the light contamination 

comes from scattering off the white walls in the room. 

However, it was determined that the scattering was sufficiently low that it had a negligible effect on the 

viewing performance. In contrast, display #2 is often 

used in a conference room format, where some overhead 

lights are turned on so that the audience can take notes. 

Although the room designers were careful to use dark 

materials for the reflective surfaces, some of the overhead fluorescent light was directly illuminating the 

presentation screen. The light contamination from the 

fluorescent lights produced a 63 % increase in the screen 

luminance (due to background noise), the contrast ratio 

dropped to 2.7 (from 1255), the color gamut area 

dropped to 3.3 % (from 36 %), and the color gamut volume was reduced to 8 % of its original value. Therefore, 

the ambient lighting severely impacted the viewability 

of the imagery. We advised the owner that this could be

largely mitigated by the use of directional or local lighting at the conference table. 

The influence of the concave geometry of the multiwall CAVE system (display #3) was also evaluated for

light contamination from the adjacent walls. It was determined that when the adjacent walls and floor were in 

the full white state (worst case scenario), the viewing 

Figure 59. Relative contrast ratio false color map of display #2 

with the floor and side screens turned off (left image) and turned on 

(right image). Red indicates high contrast ratios.
76 NIST Applied and Computational Mathematics Division

performance of the front screen was dramatically degraded. Even when the intensity of the light from the 

adjacent walls and floor was reduced to more typical 

levels (30 % of peak white), the front screen luminance 

would increase by 5 %, the contrast ratio would decrease 

to 21 (from 1660), the color gamut area would drop to 

19 % (from 28 %), and there would be a 47 % loss in the 

color gamut volume compared to the case with no ambient illumination. Our methods were able to quantify the 

impact of the light contamination, and can be applied in 

developing solutions to minimize its impact.

Advanced immersive display systems are currently 

being developed using laser sources. The polarization 

and narrow band properties of these light sources can 

have an adverse effect on the metrology tools commonly 

used on incoherent projection systems. Therefore a 

study was also conducted to evaluate the influence of laser (and LED) light sources in characterizing immersive 

displays. It was found that higher spectral resolution (≤ 

5 nm) spectroradiometers with de-polarizing elements 

are generally needed for these light sources.

The experimental results of this study were analyzed and a paper was submitted for publication [5]. We 

will be extending our measurement of optical characteristics of displays for immersive visualization.

[1] Information Display Measurements Standard, V1.03, International Display Metrology Committee, Society of 

Information Display (2012).

[2] E. F. Kelley, K. Lang, L. D. Silverstein and M. H. Brill, 

Methodology for Estimating the Luminous Flux Based 

upon Color Primaries from Digital projection Displays, 

NISTIR 6657, January 2009.

[3] E. F. Kelley, K. Lang, L. D. Silverstein and M. H. Brill, 

Projector Flux from Primaries, Society of Information 

Display Symposium Digest of Technical Papers 40

(2009), 224-227.

[4] J. Penczek, P. A. Boynton and E. F. Kelley, Measuring 

3D Crosstalk Uniformity and its Influence on Contrast 

Ratio, Journal of the Society of Information Display 21

(June 2013), 225-230.

[5] 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, in 

review.

Texture Compression Evaluation 

and Optimization

Wesley Griffin 

Marc Olano

Texture compression is widely used in real-time rendering to reduce storage and bandwidth requirements. 

Hardware-based texture compression has not fundamentally changed since its introduction in 1999. Recently, 

however, interest has grown in improving texture compression. Our research has explored new techniques for 

reducing the bit rate for the current fixed bit rate algorithms as well as new variable bit rate algorithms that 

can be efficiently decoded in graphics hardware. This 

work benefits the rendering and visualization communities by providing a methodology for evaluating and 

optimizing texture compression. This work can be directly applied to existing projects 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. This year we presented a paper, “Objective Image Quality Assessment of Texture Compression” at the 

2014 ACM SIGGRAPH Symposium on Interactive 3D 

Graphics and Games [1]. This paper presents our new 

evaluation methodology that accounts for the two ways 

in which textures are used in rendering, which the MSE 

and PSNR measures cannot account for. We have also 

extended the paper to explore the relative effects between how textures are used to render objects [2]. The 

extended paper is currently under review in IEEE Transactions on Visualization and Computer Graphics. In this 

study, we discovered that the type of texture, combined 

with how it is used, has an impact on perceived quality 

when rendering with compressed textures.

Future work will involve implementing an optimization framework based on our evaluation methodology. 

By developing an optimization method, we can enable 

real-time rendering asset pipelines to automatically optimize texture compression rates and quality. This will 

further benefit the real-time rendering community by removing the highly subjective and time-consuming task 

of finding the right compression algorithm settings for 

textures. 

Table 2. General characteristics of the 3-D immersive display 

systems measured in this study.

Characteristic Display 

System #1

Display 

System #2

Display 

System #3

Install year 2004 2009 2013

Screen size 2.67m x 

2.07m

3.78m x 

2.13m

4-wall CAVE

(3.04m x 3.04m 

per wall)

Screen resolution1280 

x1024

1920 

x1080

1920x1924

(2 overlapping 

projectors)

Projector

3-chip 

DLP lamp 

projector

3-chip 

DLP lamp 

projector

3-chip DLP 

lamp projector

Display type Rear

projection

Front

projection Rear projection

Nominal 

measurement 

position

1.65m 

high, 

1.22m 

from front

1.46m 

high,

5.4m 

from front

1.65m high, 

1.52m from 

front
Summary of Activities for Fiscal Year 2014 77

[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, in review. 

Information Visualization for 

Complex Information Systems

Sandy Ressler

Kevin Mills (NIST ITL)

Chris Dabrowski (NIST ITL)

James Filliben (NIST ITL)

Mohamed Gueye (City College of New York)

http://www.nist.gov/itl/antd/emergent_behavior.cfm

This project aims to develop and evaluate a coherent set 

of methods to understand behavior in complex information systems, such as the Internet, computational 

grids and computing clouds. We are providing visualizations which help to convey the results of this project. 

As an extension of work done in the previous year 

we produced an animation of a network based on the 

2001 configuration of the Autonomous System (AS) 

portion of the Internet that the team uses for study. The 

graph consists of approximately 11,000 nodes and 

47,000 edges. Using an off-the-shelf open source tool 

called gephi we produced a number of visualizations 

that have helped reveal the structure of the network.

Data illustrated using gephi shown in Figure 60 was animated using alternate visualization parameters; see

Figure 61. Colors correspond to data clusters using the 

“modularity” network metric.

We intend on using developments of the cloud computing simulation system and additional network 

configurations as the source for further visualizations 

that will impact the research process. We produced a 

number of visualizations using the d3.js library to visualize and compare genetic algorithms applied to cloud 

simulation data; see Figure 62. These were done primarily by Mohammed Gueye, a NIST SURF student during 

the summer of 2014. By using d3, a highly interactive 

toolset, we were able to give researchers choices about 

which simulation run to observe and to compare different sets, both topologically and via bar graph displays.

[1] K Mills, C. Dabrowski, J. Filliben and S. Ressler, “Combining Genetic Algorithms and Simulations to Search for 

Failure Scenarios in Systems Models,” Distinguished 

Lecture, Mitre Cyber Security Technical Center, 

McLean, Virginia, October 16, 2013.

[2] K. Mills, C. Dabrowski, J. Filliben, S. Ressler and Y. 

Wan, “Predicting the Unpredictable in Complex Information Systems,” Network Science Symposium, College 

Park, Maryland, January 24, 2014.

[3] K. Mills, C. Dabrowski, J. Filliben and S. Ressler, “Combining Genetic Algorithms and Simulation to Search for 

Failure Scenarios in System Models,” Computer Science 

Interdisciplinary Seminar, George Mason University, 

February 19, 2014.

Visualizing the National 

Vulnerability Database

Sandy Ressler 

Mohamed Gueye (City College of New York)

The National Vulnerability Database contains reported 

computer vulnerabilities in a convenient single authoritative location. We have experimented with a number of 

visualizations to help security researchers better identify 

trends and to explore the data set interactively. We have 

utilized the “Keshif Browser” [1]. It allows a great deal 

Figure 60. Internet autonomous system graph circa 2001 in gephi 

tool.

Figure 61. Frames from animation of Internet autonomous system 

graph circa 2001.

 

Figure 62. Topological and bar graph visualization of simulation 

data.
78 NIST Applied and Computational Mathematics Division

of exploratory freedom as described on its web site: “It 

presents visual summaries of your data properties, such 

as who, what, when and where, in its facets and timeline. 

You can discover relations between attributes through 

exploration. Filtering follows a consistent design within 

and across facets. After each step of exploration, the 

most relevant results and data properties are shown 

first, as they are dynamically and smoothly re-ordered.”

With the browser users can filter across a variety of 

parameters, and choose among treemap, scatterplot or 

bullet graph visualizations. The browser follows the 

classic Shneiderman information seeking mantra or 

providing an “Overview” allowing “Zoom and Filter”

with “Details on Demand”. 

There are three main areas for the browser. The left 

side allows the user to filter from among all of the 

properties that comprise the basis for producing a 

vulnerability score. After selecting one or several filters, 

the list of CVE vulnerabilities that match the selected 

filters is presented on the right. The user can then select 

the particular vulnerability for closer inspection. The top 

portion of the browser displays the selected entries on a 

timeline indicating when they were reported. The three

rows of dots correspond to the three values the 

“availability-impact” parameter can occur. Finally 

lower right portion of the browser displays a list of the 

vulnerabilities that meet the filter criteria.

The illustrations in Figure 63 through Figure 65 are 

the three types of visualizations that can be produced by 

the browser: scatter plot, bullet graph, and a treemap. 

Each provides a different perspective on the data.

We also produced a calendar visualization 

displaying the quantity of vulnerabilities reported on the 

date. See Figure 66. One nice feature of this 

visualization is the ability to display the entire history of 

the NVD vulnerabilities on a single screen.

[1] http://www.cs.umd.edu/hcil/keshif, accessed 01/09/2014.

Figure 63. NVD vulnerability data displayed in the Keshif Browser.

Figure 64. NVD Data in Keshif Browser with scatterplot visualization.

Figure 65. NVD Data in Keshif Browser with bullet graph visualization.
Summary of Activities for Fiscal Year 2014 79

WebVR Graphics

Sandy Ressler 

Mohammed Gueye (City College of New York)

Tomasz Bednarz (CSIRO, Australia)

The Oculus Rift is a new virtual reality headset that is 

bringing about a renaissance for virtual reality (VR). 

The quality is relatively high and cost is low. WebVR is 

a new technology that enables web browsers to support 

VR devices “natively.” We are performing this work because it has the potential to allow wide diffusion of 

immersive scientific visualizations with very low cost 

hardware. This will benefit the larger research community at NIST that already takes advantage of immersive 

visualization and has the potential of making that community much larger. We have managed to integrate early 

versions of the X3DOM standard representation of 

graphics with a VR headset. We plan on collaborating 

with partners in Australia at CSIRO to further develop 

these immersive capabilities as they also have common 

scientific visualization needs.

VR in the web browser means that, without any additional software, we can make use of the viewer’s head 

orientation and position. The result is a display that presents the user with stereo, head-tracked images, giving 

the illusion of a first person point-of-view scene. We 

have begun to experiment with the combination of 

WebVR with our previous work on declarative Web3D. 

The results are visualizations using declarative graphics 

Figure 66. Calendar view of the NVD CVE Vulnerability data set.
80 NIST Applied and Computational Mathematics Division

that can function with the new generation of virtual reality headsets. See Figure 67.

In addition to geometric scenes we are experimenting with 360 degree video sources. We map the video 

onto both the inside and outside surfaces of a sphere; see 

Figure 68. Placing the viewer inside the sphere results in 

a video image warped to appear “correct” to the viewer. 

The sphere and video texture mapping are accomplished 

using standard X3DOM declarative constructs. 

The intent is to have the ability to create 360 panoramic videos that play inside of web pages that are headtracked. This will be extended via the use of WebRTC 

to the ability to have multiple collaborators sharing a 

single video space, which will be done in collaboration 

to Thomas Bednarz (CSIRO - Australia) for mining or 

other applications in a NIST/CSIRO collaboration. 

[1] x3dom web page posting; accessed 01/08/2015

Figure 67. X3DOM scene functioning with Oculus Rift headset [1].

Figure 68. 360 degree video viewed from inside of sphere.
Summary of Activities for Fiscal Year 2014 81

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.

Tamper-Resistant Cryptographic 

Hardware using Isolated Qubits

Yi-Kai Liu

See page 15.

Quantum Information Science

Scott Glancy

Emanuel Knill

Adam Keith (University of Colorado)

Jim van Meter (University of Colorado)

Peter Wills (University of Colorado)

Kevin Coakley (NIST ITL)

Sae Woo Nam (NIST PL)

Dietrich Leibfried (NIST PL)

David Wineland (NIST PL)

David Pappas (NIST PL)

Gerardo Ortiz (Indiana University)

Paul Kwiat (University of Illinois)

The traditional information units of classical computing 

are 0/1-valued bits, which may be realized as distinguishable states of physical systems. Quantum 

information science investigates the properties and applications of quantum bits. Formally, quantum bits have 

pure states defined as superpositions of two distinguishable states. Quantum bits promise to be powerful 

information processing units whose potential is realized 

when they are coupled by means of quantum gates, 

which generalize classical circuit elements. Applications include efficient algorithms for factoring integers 

and for physics simulation, protocols for secure communication, and significantly improved measurement 

precision. In addition, there is the potential for illuminating the foundations of physics, in particular the 

universality of quantum mechanics and field theory. 

In the last few years, there has been tremendous experimental progress demonstrating long-lived quantum 

bits in diverse systems, including individually trapped 

atoms, superconducting circuit elements and various 

other solid state devices. Thus, we currently expect that 

quantum information processing will eventually be realized on large scales. Nevertheless, there are significant 

obstacles in realizing the benefits of quantum information processing. Perhaps the most challenging 

obstacles are to experimentally construct multi-qubit 

systems whose quantum states are both stable and robustly manipulable by quantum gates. One reason the 

two requirements are difficult to meet is that stability requires good isolation from the environment, but 

manipulatability involves interaction with an external 

controller. 

Our work in quantum information science aims to 

characterize quantum devices in terms of their potential 

for information processing, determine ways of exploiting quantum control for better measurements of physical 

quantities such as time and space, and contribute to our 

understanding of the power and limitations of quantum 

physics as it relates to information extraction and processing. In this spirit, we investigate a broad range of 

subjects.

Many applications of quantum mechanics to communication and cryptography rely on experimental tests 

of Bell inequalities. These tests also provide the strongest evidence against local realism (LR) as a possible 

explanation of quantum non-determinism. While there 

have been many experiments demonstrating the required 

violation of Bell inequalities, so-far they have suffered 

from loopholes and problems with quantifying the evidence against LR. We have developed a powerful 

strategy for analyzing Bell-test data that can quantify the 

evidence against LR in a configuration-independent 

way. Two complicating features of many current Bell 

tests is that the required random settings choices cannot 

be changed fast enough and the data obtained at each 

setting choice consists of many time-tagged detections. 
82 NIST Applied and Computational Mathematics Division

For comparison, in text-book Bell tests, exactly one detection is recorded at each setting choice. We have 

developed a Bell-test analysis method that can take advantage of the many detections recorded at one setting 

without being deceived by loopholes. We have applied 

this method to Bell-test data from P. Kwiat’s lab at 

UIUC to show that it violates LR without being subject 

to the so-called detection loophole. A conventional analysis did not show this violation.

The statistical principles underlying our Bell-test 

analysis are general and have the potential for simplifying the analysis of data at high significance levels 

without making approximations. To investigate the regime of application of our methods, we are considering 

the simple problem of estimating the bias of the bits in a 

sequence of independent and identical random bits. We 

expected that a comparison of methods would require 

Monte-Carlo simulations, but found that analytical expressions for the performance were available even for 

our nominally adaptive methods. Once we have completed the comparison of methods for bit flips, we will 

consider the problem of estimating the mean of a 

bounded random variable.

In collaboration with John Bollinger’s team in the 

NIST Ion Storage Group, we adapted a classical simulator for ions in a Penning trap with laser cooling to 

explore the thermodynamic temperature and non-linear 

behavior of axial and planar modes of a two-dimensional ion crystal. The goal is to determine 

experimentally difficult-to-access mode temperatures as 

a function of trap and laser parameters in the hope of 

obtaining colder and more stable crystals. This may help 

with planned quantum simulations and demonstrations 

of quantum correlations in this system.

Particles carrying quantum information are indispensable in quantum information science and emerge as 

fundamental excitations in most quantum condensed 

matter systems. In some systems these excitations are 

expected to take the form of non-abelian anyons, which 

may provide naturally protected subsystems for storing 

quantum information. A fundamental question is 

whether the different types of particle-like excitations 

can be described in a unified framework that captures 

the features of both traditional particles (bosons and fermions) as well as anyons. We have started collaboration 

with Gerado Ortiz of Indiana University to explore the 

possibility of using algebraic quantum theory for such a 

framework.

Measurement and information processing operates 

on increasingly small and fast scales where relativistic 

effects cannot be neglected. The emerging field of relativistic quantum information processing aims to explore 

these effects for precise measurement and control of information. In this spirit, we are analyzing proposed 

Heisenberg uncertainty relationships based on algebraic 

quantum field theory on curved space-time backgrounds. While they have the expected form, their 

application requires computing correlations of energymomentum operators. We are planning on computing 

these correlations for some relevant situations such as 

gravitational wave detection with laser interferometry. 

For the algebraic approach to be generally useful, it 

should match the expected shot-noise limits, and we expect that it will do so. 

[1] E. Cobanera, G. Ortiz and E. Knill, A Solution to the 

Non-Abelian Duality Problem, Nuclear Physics B 877

(2013), 574-597.

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

Physical Review A 88 (2013), 052119.

[3] M. Mullan and E. Knill, Simulating and Optimizing 

Atomic Clock Evolution, Physical Review A 90 (2014), 

042310.

[4] A. C. Wilson, Y. Colombe, K. R. Brown, E. Knill, D. 

Leibfried and D. J. Wineland, Tunable Spin-Spin Interactions and Entanglement of Ions in Separate Wells, 

Nature 512 (2014), 57-60.

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

Zhang, Bell Inequalities for Continuously Emitting 

Sources, in review.

Quantum Estimation Theory and 

Applications

Scott Glancy

Adam Keith

Emanuel Knill

Nadav Kravitz (University of Maryland)

Kevin Coakley (NIST ITL)

John Gaebler (NIST PML)

Konrad Lehnert (NIST PML)

Yiheng Lin (NIST PML)

Ting Rei Tan (NIST PML)

Yong Wan (NIST PML)

Will Kindel (University of Colorado)

Hsiang-Sheng Ku (University of Colorado)

Many emerging technologies will exploit quantum mechanical effects to enhance metrology, computation, and 

communication. Developing these technologies requires 

improved methods to measure the state of quantum systems. Quantum 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.

Full quantum estimation can be a demanding task, 

requiring a large number of different measurements to 

be performed on (independently prepared copies) of the 
Summary of Activities for Fiscal Year 2014 83

quantum system and requiring 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 sub-set of all quantum 

states, such as those states that have Gaussian probability distributions for measurement results. We have

developed two algorithms for estimating these Gaussian 

states that are orders of magnitude faster than full quantum state estimation and can be applied to data sets that 

are much too large to be analyzed with full quantum 

state estimation. One is an almost linear estimator that 

computes experimental means of simple functions of 

measurement data to estimate desired quantities. The 

other uses a maximum likelihood technique to compute 

a covariance matrix of the quantum state. The algorithms have been tested on simulated data and applied in 

an experiment that entangled microwave signals traveling through superconducting circuits in the JILA 

laboratory of Konrad Lehnert [1]. Our new algorithms 

will be useful to many experiments on quantum optics 

and nano-mechanical resonators. We are preparing a report detailing the two algorithms and comparing their 

performance.

NIST’s 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 trapped ion quantum computers. (NIST 

trapped ion experiments have reported a fidelity of 

99.9998 % for single qubit logic operations [2].) Working with the Ion Storage Group, we previously 

developed linear methods for inferring states of ions in 

Pauli traps from fluorescence histograms without making assumptions on the histogram shapes. 

Conventionally, the histograms are modeled as Poissonian distributions, but with the newer traps, this 

assumption fails at a significant level. The method was 

used to determine the fidelity of a Bell state prepared 

without bringing ions into the same potential well. The 

results from this experiment have now been published in 

Nature [3]. We are standardizing analysis protocols so 

that they can be used routinely for determining ion states 

from histograms and to integrate these protocols with 

the software that controls the trapped ion experiments.

During the next year we will be publicly releasing 

quantum estimation software that has been used in several NIST experiments. Algorithms that we have

developed will be incorporated in to an open source 

toolbox such as the one being developed by the Quantum Toolbox in Python (QuTiP) project20, making them 

available to researchers around the world.

[1] H. S. Ku, W. F. Kindel, F. Mallet, S. Glancy, K. D. Irwin, 

G. C. Hilton, L. R. Vale and K. W. Lehnert, Generating 

 

20 http://qutip.org/

and Verifying Entangled Itinerant Microwave Fields with 

Efficient and Independent Measurements, in review.

[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 10-4in a Trapped Ion, 

Physical Review A 84 (2011), 030303(R).

[3] A. C. Wilson, Y. Colombe, K. R. Brown, E. Knill, D. 

Leibfried and D. J. Wineland, Tunable Spin-Spin Interactions and Entanglement of Ions in Separate Wells, Nature

512 (2014), 57-60.

Phase Retrieval and Quantum State 

Tomography 

Yi-Kai Liu

Felix Krahmer (University of Göttingen)

Phase retrieval is the task of learning an unknown vector 

x, given measurements of the form |a

T

x|

2 where the vectors a are known. (That is, each measurement projects x

onto the direction a, and returns the modulus, but not the 

phase. One wants to reconstruct these phases, in order to 

estimate x.) Recently, new algorithms for phase retrieval have been developed, using techniques from 

compressed sensing, such as random measurements and 

convex optimization. These algorithms have nice theoretical properties, but further work is needed to make 

them useful in practice.

Two major applications of phase retrieval are X-ray 

crystallography and quantum state tomography. In the 

context of quantum state tomography, phase retrieval 

has some advantages over other approaches, because it 

naturally incorporates experimental measurements that 

project onto the eigenbasis of each observable. However, phase retrieval also has some disadvantages over 

other methods: it is not as well-understood, and it seems 

to require complicated measurements, which are difficult to implement in an experiment.

We are studying phase retrieval using simple classes of measurements (e.g., independently sampled 

Bernoulli random vectors). Here it is known that phase 

retrieval is technically impossible, in that there exist 

pathological examples of vectors (e.g., the standard basis vectors) that cannot be distinguished from one 

another using these measurements. We identify a surprisingly large class of vectors that can be recovered in 

this setting, namely “flat” vectors x that satisfy |x|∞ ≤ 

c|x|2, where c is some sufficiently small constant. For 

these “flat” vectors, we can show that phase retrieval is 

possible in an information-theoretic sense, and we are 

currently trying to give a computationally efficient 

method, using a convex relaxation known as PhaseLift. 

A future goal of this project is to develop methods 

for quantum state tomography based on phase retrieval, 
84 NIST Applied and Computational Mathematics Division

using measurements that are easy to implement in experiments. While random Bernoulli measurements are 

not suitable for this purpose, we believe that our approach can be adapted and extended to other classes of 

measurements, such as Fourier measurements with random phase factors, which are easier to implement.

[1] F. Krahmer and Y.-K. Liu, Phase Retrieval using Random 

Bernoulli Measurements, in preparation.

Random Number Generation Based 

on Bell Inequality Violation

Scott Glancy

Stephen Jordan

Manny Knill

Paulina Kuo

Yi-Kai Liu

Alan Mink (Wagner Resources)

Xiao Tang

Lawrence Bassham (NIST ITL)

Joshua Bienfang (NIST PML)

Michaela Iorga (NIST ITL)

Alan Migdall (NIST PML)

Saewoo Nam (NIST PML)

Rene Peralta (NIST ITL)

Andrew Rukhin (NIST ITL)

Random strings of bits are a fundamental resource for 

cryptography whose security is notoriously difficult to 

test. A string of bits may pass all statistical tests of randomness and yet be useless cryptographically; it could 

be a uniformly random string already known by an adversary. Remarkably, it is possible to certify that certain 

measurement outcomes in quantum experiments could 

not have been known ahead of time. This can be 

achieved using experiments called Bell tests in 

which pairs of entangled 

photons are sent to wellseparated sites and measured. The observed 

correlations between the 

measurement outcomes 

can be used to certify the 

presence of fresh randomness. The security is 

proven as a direct consequence of the 

empirically observed 

correlations and the assumptions that the initial 

random seed is secure 

and that signals cannot 

 

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

travel faster than light. The internal workings of the device needn’t be trusted. This uniquely quantummechanical form of fundamental protection against device failure and tampering is known as deviceindependent security.

The development of hardware achieving device-independent security is a challenge at the fringes of 

feasibility with current photonic techniques. To satisfy 

the conditions needed for the security proofs, it is necessary to develop and integrate fast, high-efficiency 

photon detectors, optical switches, and entangled-photon generators. Researchers in ACMD and several other 

NIST divisions are collaborating on a NIST Innovations 

in Measurement Science project to do this. Eventually, 

the resulting hardware may be put into service for cryptographic applications. In the meantime, a prototype 

random bit beacon at NIST is currently serving time 

stamped and digitally signed strings of random bits over 

the web21. The bits currently being served are generated 

by conventional hardware without device-independent 

security. A number of beacon-based cryptographic protocols for e-commerce and privacy protection have been 

proposed. These can now be tested in practice using the 

NIST beacon.

The Bell experiment needs several additional elements to form a complete cryptographic resource, some 

of which are illustrated in Figure 69. These include a 

source of random numbers to use as the initial seed, software for analyzing the outcomes of the experiment to 

certify the presence of fresh randomness, software to extract uniformly distributed strings of bits from the 

measurement outcomes, and technology to publish these 

strings over the internet. Division expertise has been 

used to develop these elements and to do theoretical and 

experimental work related to the Bell experiment itself.

This year, ACMD researchers developed a loophole-free method to analyze data from Bell experiments 

that produce entangled photons distributed randomly in 

time [1]. The analysis allows high confidence rejection 

of the hypothesis that randomness generated in the Bell 

experiment could have been known or predicted by a 

hacker. Also, ACMD researchers have in the past year 

tested two methods for generating entangled photons 

and capturing them in optical fiber with high efficiency: 

one based on spontaneous parametric downconversion 

Figure 69. Post-processing for the Bell Measurent based quantum 

random number generation project.

Figure 70. Paulina Kuo is testing methods for generating 

entangled photons.
Summary of Activities for Fiscal Year 2014 85

[2], and one based on four-wave mixing using a micro 

toroid. In addition, this year saw the completion of a 

code-review performed within ACMD on software for 

distilling secure random bits from the experimental output data produced by the Bell tests.

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

Zhang, Bell Inequalities for Continuously Emitting 

Sources. arXiv:1409.7732 (2014)

[2] P. S. Kuo, J. S. Pelc, O. Slattery, L. Ma and X. Tang, Domain-engineered PPLN for Entangled Photon Generation 

and Other Quantum Information Applications, Proceedings of the SPIE 9136 (2014), 913403.

Computational Complexity of 

Quantum Field Theory

Stephen Jordan

Keith Lee (University of Toronto)

John Preskill (Caltech)

Hari Krovi (Raytheon/BBN)

Particles and fields are central objects of study in both 

classical and quantum physics. Classically, the instantaneous state of a point particle can be fully specified by 

just six numbers: its three position coordinates and its 

three components of momentum. In contrast, a field is in 

principle determined by infinitely many numbers: its 

values at every point in space. This makes the quantum 

dynamics of fields complex and difficult to analyze 

mathematically. This project seeks to understand these 

difficulties from a computational complexity perspective. In particular we ask two main questions. First, can 

classical computers efficiently simulate the dynamics of 

quantum fields? Our evidence suggests that they cannot, 

in general. Second, can quantum computers (once they 

are built) efficiently simulate the dynamics of quantum 

fields? Our evidence so far suggests they can.

So far, we have developed polynomial-time quantum algorithms to simulate two simple quantum field 

theories (massive phi-fourth theory and the massive 

Gross-Neveu model) within the quantum circuit model 

[1, 2]. These results suggest that, despite the additional 

mathematical complications, from a computational 

complexity point of view, quantum field theories are not 

fundamentally more powerful than the quantum dynamics of fixed numbers of particles (as described by 

Schrödinger’s equation). Furthermore, upon successful

construction of large-scale quantum computers, these algorithms can be used to obtain predictions that can then 

be compared with the outcomes of particle-accelerator 

experiments.

The fields in nature can be classified as either Fermionic or Bosonic and as either massive or massless. 

The quantum field theories for which we have developed quantum simulation algorithms are a massive 

Bosonic theory (phi-fourth) and a massive Fermionic 

theory (Gross-Neveu). One of our current research directions is to investigate whether quantum computers 

can efficiently simulate the massless case. If so, we 

would have the main ingredients necessary to simulate 

the Standard Model, which is the current most widely 

accepted model of fundamental physics, incorporating 

all known forces other than gravity into a quantum field 

theory framework.

Currently, we are compiling formal evidence that 

classical computers cannot simulate quantum field theories efficiently. Specifically, we are developing a proof 

that a certain formalized quantum field theory simulation problem is “BQP-hard.” This means that any 

problem solvable in polynomial time by a quantum computer can be converted into an instance of the quantum 

field theory simulation problem. Thus, if one could simulate quantum field theory efficiently on a classical 

computer, then one could simulate quantum computers 

efficiently on a classical computer. It is generally believed that one cannot simulate quantum computers on 

classical computers. Therefore, such a BQP-hardness result can be viewed as evidence that classical computers 

cannot simulate the dynamics of quantum fields with 

polynomial runtime on the hardest instances.

[1] S. P. Jordan, K. S. M. Lee and J. Preskill. Quantum Computation of Scattering in Scalar Quantum Field Theories, 

Quantum Information and Computation 14:11/12 (2014), 

1014-1080.

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

arXiv:1404.7115 (2014).

Quantum Adiabatic Optimization

Stephen Jordan

Michael Jarret (University Maryland)

Quantum computers do not offer speedup for all computational problems. For some problems, such as factoring 

integers, quantum algorithms promise exponential 

speedup over the fastest classical algorithms. For other 

problems, such as computing sums modulo 2, they are 

known to offer no advantage over classical computation. 

Due to the widespread applications of optimization, the 

question whether quantum algorithms offer substantial 

speedup for optimization has long been an area of intense research interest.

In 1999, Farhi et al. proposed an intriguing framework for the design of quantum optimization algorithms 

called adiabatic quantum computing. Quantum adiabatic 

algorithms are easy to design and are guaranteed to find 

the optimum given sufficient runtime. The key difficulty 

is determining how this runtime depends on the features 

of the objective function of the optimization problem. 
86 NIST Applied and Computational Mathematics Division

The runtime of an adiabatic quantum algorithm is determined by the gap between the lowest and second lowest 

eigenvalues of a matrix called the Hamiltonian. The 

Hamiltonian is an exponentially high dimensional matrix, so for problem sizes of practical interest it is 

infeasible to calculate the eigenvalue gap numerically. 

Due to the primitive nature of present-day quantum 

computational hardware it is also extremely difficult to 

study the eigenvalue gap experimentally. Thus there is a 

great need for mathematical tools to analyze eigenvalue 

gaps of Hamiltonians.

In this project we are investigating the effect that 

local minima in the objective function have on the eigenvalue gap of the resulting Hamiltonian. The 

strongest known upper bound on the runtime of adiabatic algorithms scales as one over the square of the 

eigenvalue gap. Surprisingly, it turns out that even for 

objective functions without local minima (whose global 

minima are easy to find classically by gradient descent), 

this eigenvalue gap can be exponentially small [1]. On 

the other hand, for convex optimization problems in low 

dimension or high symmetry, we have proven that the 

gap cannot be exponentially small [2]. In current work, 

we are importing tools from spectral graph theory to 

tighten and generalize these bounds.

[1] M. Jarret and S. P. Jordan, Adiabatic Optimization without Local Minima, Quantum Information and 

Computation 14:3/4 (2015), 0181-0199.

[2] M. Jarret and S. P. Jordan. The Fundamental Gap for a 

class of Schrödinger Operators on Path and Hypercube 

graphs, Journal of Mathematical Physics 55:5 (2014), 

052104.

Quantum Computation and Knot 

Theory

Stephen Jordan

Gorjan Alagic (University of Copenhagen)

Stacey Jeffery (Caltech)

Aniruddha Bapat (Caltech)

Michael Jarret (University of Maryland)

A knot is an embedding of the circle into three-dimensional space. More generally, a link is an embedding of 

one or more circles into three-dimensional space. One of 

the central problems in low-dimensional topology is, 

given a pair of links, determine whether they are equivalent. That is, can one be smoothly transformed into the 

other without cutting strands or passing them through 

one another? Mathematically and computationally, this 

is a very difficult problem. Link invariants provide a partial solution. These are functions that take links as input 

and produce easy-to-distinguish objects (such as numbers or polynomials) as output. Link invariants take the 

same value on equivalent links. Thus, evaluating an invariant of a pair of links and obtaining different outputs 

is an effective means of proving that two links are topologically inequivalent.

Amazingly, it turns out that many of the known link 

invariants come from quantum mechanics. Specifically, 

matrices that satisfy the Yang-Baxter equation describe 

the braiding of certain quantum particles confined to two 

dimensions and also give rise to many of the most important link invariants. As a result, the theory of 

quantum information and computation can be used to 

help characterize both the power of link invariants for 

distinguishing links and the computational complexity 

of evaluating the link invariants.

A matrix satisfying the Yang-Baxter equation can 

be interpreted as a quantum logic gate. In the case that 

the quantum logic gate is universal for quantum computation (analogous to the universality of the NAND gate 

for classical computation), one can show that corresponding link invariant is BQP-complete to 

approximate. Thus, classical algorithms to approximate 

the link invariant almost certainly require exponential 

runtime. Building upon previous classification work of 

Hietarinta and Dye, we have shown that no 4x4 solution 

to the Yang-Baxter equation is a universal quantum gate 

[1]. This is bad news if one wishes to build a quantum 

computer using these gates, but is good news if one 

wishes to approximate the corresponding link invariants 

on classical computers. In recent work, not yet published, we have also proven that Yang-Baxter matrices 

can only yield nontrivial knot invariants if the corresponding quantum gates generate quantum 

entanglement. This may be of use in future work searching for new link invariants. In addition, we have 

recently proposed an approach to cryptographically obfuscating quantum and classical logic circuits using the 

topological equivalences of braids that the Yang-Baxter 

equation represents [2].

[1] G. Alagic, A. Bapat and S. Jordan. Classical Simulation 

of Yang-Baxter gGtes, in Proceedings of the Ninth Conference on Theory of Quantum Computation, 

Communication, and Cryptography (TQC2014), Singapore, May 21-23, 2014, 161-175.

[2] G. Alagic, S. Jeffery and S. Jordan, Partial-indistinguishability Obfuscation using Braids, in Proceedings of the 

Ninth Conference on Theory of Quantum Computation, 

Communication, and Cryptography (TQC2014), Singapore, May 21-23, 2014, 141-160.
Summary of Activities for Fiscal Year 2014 87

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 crucial tool for protecting 

the confidentiality and integrity of data transmitted over 

the Internet. Large-scale quantum computers, if they are 

ever built, would break many of the public key cryptosystems that are currently in use, such as RSA and 

elliptic curve cryptosystems. Researchers at NIST have 

been investigating possible replacements for these cryptosystems that would be secure against quantum attacks 

– so-called “post-quantum” cryptosystems. The goal of 

this project is to prepare for the possible development of 

standards in this area. 

Existing proposals for post-quantum cryptosystems 

include lattice-based cryptosystems (such as NTRU), 

code-based cryptosystems (such as McEliece), multivariate cryptosystems (such as HFE and unbalanced oilvinegar), hash-based signatures (such as Merkle trees), 

and key exchange protocols based on elliptic curve isogenies. However, all of these proposals face significant 

open questions regarding their security and practical feasibility.

In the past year we have continued to study these 

issues. We have obtained new results on information-set 

decoding of structured MDPC codes, differential properties of the HFE cryptosystem, and the security of the 

ABC multivariate encryption scheme. We have also updated our survey of the research literature, focusing on 

matrix multivariate encryption, worst-case-to-averagecase reductions for the learning-with-errors problem, 

and various techniques for cryptanalysis.

In addition, we have engaged with the broader cryptography community. Lily Chen gave an invited talk at 

this year’s PQCrypto conference, and Dustin Moody, 

Ray Perlner and Daniel Smith-Tone presented their research at that same conference. Lily Chen and Ray 

Perlner also contributed to a whitepaper on quantumsafe cryptography produced by the European Telecommunications Standards Institute (ETSI). Stephen Jordan 

taught a short course on quantum algorithms at NIST, 

and together with Yi-Kai Liu organized the kickoff 

workshop for the NIST – University of Maryland Joint 

Center for Quantum Information and Computer Science 

(QuICS). Finally, this year we hosted visits by Bo-yin 

Yang and Jintai Ding (on multivariate cryptography) 

and Vadim Lyubashevsky (on lattice-based cryptography), and we are preparing to host a workshop on postquantum cryptography (co-located with the PKC conference) in April of 2015. 

[1] T. Daniels and D. Smith-Tone, Differential Properties of 

the HFE Cryptosystem, in Proceedings of PQ Crypto 

2014, Lecture Notes in Computer Science Volume 8772

(2014), 59-75.

[2] D. Moody, R. Perlner and D. Smith-Tone, An Asymptotically Optimal Structural Attack on the ABC Multivariate 

Encryption Scheme, in Proceedings of PQCrypto 2014, 

Lecture Notes in Computer Science 8772 (2014), 180-

196.

[3] R. Perlner, Optimizing Information Set Decoding Algorithms to Attack Cyclosymmetric MDPC Codes, in 

Proceedings of PQCrypto 2014, Lecture Notes in Computer Science 772 (2014), 220-228.

High-Speed Error Correction Codes 

for Quantum Key Distribution

Alan Mink (Wagner Resources)

Anastase Nakassis (NIST ITL)

Quantuminformation 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 involve 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 reconcile and correct errors between their bit 

sequences without exposing the value of their bits. 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 
88 NIST Applied and Computational Mathematics Division

minimized and kept below a given limit to extract a secret and quantum data retransmission is not possible. 

The research community is pursuing the next generation of QKD systems, ones that can attain higher 

speeds and longer distances. Our focus is on speed. 

Moving from the current Mb/s to the Gb/s secure key 

range will require highly optimized and parallel implementations of QKD post processing algorithms. The 

one-way EC algorithms, low density parity check 

(LDPC) and Polar codes tend to be coarse grained computations in that a given data set does not need to 

communicate until a solution is obtained. Such algorithms are amenable to parallel implementation. Each 

data set can be assigned to a separate computation engine, which would operate independently in parallel, but 

each result must be collected sequentially to maintain 

the required synchronization between Alice and Bob’s 

bits. Also a single communication round trip reduces delays, a benefit as the distance between Alice and Bob 

increases.

For a LDPC error correction algorithm suited for 

QKD applications [1], we have obtained a processing 

rate of up to 200 Mb/s for a GPU implementation. Although in the reasonable QKD operating area the 

processing rate is in the 27 to 117 Mb/s range. GPU 

streaming did not provide any throughput increase for 

our implementation, possibly due to the overhead incurred from the increase in the CPU pthreads required to 

support GPU streaming and partly due to the overhead 

incurred by spawning multiple GPU kernels. Also, for 

streaming, the kernels’ execute times are staggered and 

not completely in parallel. Specific GPU instructions 

have less performance effect for newer architectures, especially when data items are accessed only once and not 

reused, as is the case for LDPC, from caches dedicated 

to those instructions. Thus, the potential for GPUs to 

provide Gb/s LDPC error correction, although possible, 

seems less feasible, requiring up to 37 GPU boards using 

our LDPC implementation vs. the more palatable 10 

GPU boards previously speculated.

Polar coding is the most recent scheme in the quest 

for an error correction code that approaches the Shannon 

limit, has a simple structure, and admits fast decoders. As such, it is an interesting candidate for QKD. We 

developed three configurations for adopting Polar codes 

for the QKD protocol [2]. We also experimented with a 

current analytical method (Z-values) to design a Polar 

code (generate the Frozen bit set) and found that it was 

not very Shannon efficient. Our approach using simulation was marginally better (~5 %) than the Shannon 

efficiencies cited in the literature and we developed code 

designs for additional QKD operating points. But such a 

simulation approach is not scalable, because as N grows 

the process of finding which bits to freeze takes longer 

(N log N) and requires more simulation iterations. Furthermore, we found that as N grows, error correction 

failures increased. We speculate that this is due to floating point precision problems, since probability products 

have long chains and quickly approach 50 %, a value 

indicating no information. The difference between 50 %

and the computed value can grow asymptotically small 

very quickly, even with extended precision. 

Attached processors, such as FPGAs and GPUs, 

have proven to provide performance enhancements for 

implementations of LDPC and Polar error correction algorithms. Our experiments have so far achieved 

through-put rates up to 200 Mb/s, but not yet 1 Gb/s. 

Furthermore, our error correction efficiencies obtained 

for QKD operating points are more in the 40 % to 60 %

range above the Shannon limit rather than the 10 % to 

20 % range that is preferred. However, we are able to 

design codes with low failure rates, below 2 %.

[1] A. Mink and A. Nakassis, LDPC Error Correction for 

Gbit/s QKD, in Proceedings of the SPIE: Defense Security & Sensing 9123 (May 2014), 912304-1.

[2] A. Nakassis and A. Mink, Polar Codes in a QKD Environment, in Proceedings of the SPIE: Defense Security & 

Sensing 9123 (May 2014), 912305-1.

Quantum Communication

Xiao Tang

Paulina Kuo

Oliver Slattery

Lijun Ma (Theiss Research)

Weijian Chen (Washington University St. Louis)

Barry Hershman

Alan Mink (Wagner Resources)

Security is a major issue in current communication systems and networks. Quantum communication can 

provide unconditional security that is guaranteed by the 

fundamental laws of physics rather than mathematical or 

algorithmic computational complexity. In addition, 

quantum communication can transmit quantum states 

from one location to another, which is an important capability for any quantum information system. Our 

current quantum research areas include single photon 

creation, transmission, storage, transduction and detection. These are the fundamental building blocks for the 

secure quantum communications systems of the future. 

In such systems, one will encode information into strategically created single photons (flying qubits), transmit 

them and interface them with an atomic quantum 

memory (stationary qubits) for storage and processing. 

A typical example of such a system is a quantum repeater that can connect quantum computers or be used 

in quantum communication networks of the future. 

Previous work. In previous years, the ITL quantum 

communication team focused on the development of single photon frequency conversion devices including up-
Summary of Activities for Fiscal Year 2014 89

conversion devices and down-conversion single photon 

sources. An up-conversion device converts single photons from the telecommunication bands (lower energy) 

to the visible or near visible bands (higher energy) for 

high efficiency, low noise and high speed detection. A 

frequency down-conversion device is usually used to 

generate correlated or entangled single photon pairs. In 

FY 2013 we undertook work to improve the performance of the devices, and to expand their applications. 

Four such efforts: “Frequency correlated Bi-photon 

spectroscopy”, “Reducing noise in single-photon-level 

frequency conversion”, “Spectral response of an upconversion detector and spectrometer,” and “Two-photon 

interference with continuous-wave multi-mode coherent 

light” [1] were completed and published. In addition, the 

team continuously worked to transfer their technology 

to US industry for commercialization through the NIST 

Small Business Innovative Research (SBIR) program.

Recent developments. Based on the previous work, in 

FY 2014, the team continued the work in the areas of 

photon down-conversion devices including: 

 a photon pair source near 1550 nm for the NIST 

IMS Quantum Randomness project; 

 another photon pair source at 1310 nm and 895 nm 

with narrow spectral linewidth; and 

 a quantum interface based on frequency upconversion device. 

In FY 2014, the team also expanded their research areas 

to include: 

 quantum memory based on electromagnetically induced transparency (EIT) in a warm cesium cell; 

 a photon pair source based on four-wave mixing using a micro toroid; 

 study of single photon emitters in diamond thinfilm substrates containing nitrogen vacancies (NV) 

centers, silicon vacancies (SiV) centers or nickel 

centers using an in-house built confocal microscope; 

 support for the quantum randomness project and research in QKD protocols and standards; and 

 technology transfer of a Bragg-grating enhanced 

single photon source. 

Current developments are as follows:

1. The team jointly worked with colleagues in the NIST 

Physical Measurement Laboratory (PML) on the 

IMS 2013 project entitled “Quantum Randomness as 

a Secure Resource”. Our responsibility is to develop 

an entangled photon pair source that is suitable for a 

loophole-free Bell test. Paulina Kuo leads the design 

and implementation for the photon pair source at 

1535 nm and 1575 nm, which is based on Type II 

SPDC in a domain-engineered PPLN chip with a 

pump at 775 nm. The work is continued from last 

year and significant progress has been achieved this 

year. Difference frequency generation (DFG, a 

seeded SPDC) was demonstrated [2]. When the 

source is completed, it will also be a candidate for 

use in our future quantum repeater.

2. A non-degenerate photon pair source based on SPDC 

was developed in the previous years by Oliver Slattery. The source generates photon pairs at 1310 nm 

and 895 nm that was used to demonstrate Frequency 

Correlated Bi-Photon Spectroscopy in FY2013. The 

source can also be used to interface “flying qubits” 

(1310 nm for long distance transmission) and “stationary qubits” (895nm for storage and processing in 

Figure 71. Quantum communications project team (from left to right): Xiao Tang, Barry Hershman, Paulina Kuo, Alan Mink, Lijun Ma and 

Oliver Slattery.
90 NIST Applied and Computational Mathematics Division

a cesium (Cs) atomic system). In this case, the bandwidth of 895-nm photons must be comparable with 

that of the cesium D1 line. A common way to solve 

the problem is to place the device in a cavity which 

is independently locked to an atomic transition line. 

The major progress this year is that the cavity is stably locked to the Cs D1 line and multi-mode narrow 

band SPDC photon pairs were generated. Ongoing 

work includes full characterization of the SPDC generated pairs and investigating alternative cavity 

configurations for optimal interfacing with other elements (e.g., quantum memory) of the project. 

3. An upconversion device that converts single photons 

at 1550 nm to 852 nm using a pump at 1892 nm was 

constructed By Paulina Kuo. This device can be used 

as a detector for telecom band single photons, as well 

as a quantum interface to connect photons at 1550 

nm (flying qubits) and the cesium atomic D2 transition line at 852 nm (stationary qubits). Currently the 

device implementation is completed. The conversion 

efficiency has reached 7 % and the noise level is reduced to an acceptable level. 

4. A quantum memory is a device that can store the 

quantum state of a particle (e.g., a photon) and retrieve it on demand. It is a key component in many 

quantum information applications such as quantum 

repeaters. Among the variety of approaches to date, 

quantum memory based on electromagnetically induced transparency (EIT) stands out as the most 

promising and suitable approach for our current application. The team had prepared to launch this 

project some time ago, but were only able to start it 

in January 2014 when Lijun Ma re-joined the team. 

The experimental setup for an EIT-based quantum 

memory system with a warm cesium cell (≈60 oC) 

has been successfully completed. With this system, 

the slow light effect based on EIT was recently 

demonstrated. 

5. In March 2014, the team started a joint research effort with Washington University in St. Louis 

(WUSTL), to study entangled photon pair generation 

based on four-wave mixing (FWM). Weijian Chen, 

a student from WUSTL performed the experiment at 

NIST using a micro toroid fabricated at WUSTL. 

The micro toroid is made of silica and forms an optical cavity with extremely high quality factor (Q) 

value as high as 108, which enables us to develop 

photon pair sources with very narrow bandwidth 

comparable to that of atomic transition lines. Furthermore, the optical coupling between the toroid 

and the taped fiber was demonstrated to be nearly 

lossless by other researchers. This unique feature allows us to develop a photon pair source with a very 

high so called “heralded efficiency.” Thus, this 

source is a promising candidate for use in loopholefree Bell tests, which is a key component of the NIST 

IMS Quantum Randomness project. Recently, photon pair generations near 1550 nm from a micro 

toroid was observed at weak light power levels. 

6. Confocal microscopes are commonly used for mapping nano-diamond (ND) samples and for detecting 

and spectrally characterizing single-photon emitters 

in ND. In this FY, Oliver Slattery built an in-house 

confocal microscope in our lab. It has been used to 

study Nitrogen-Vacancy (NV), Silicon-Vacancy 

(SiV) and Nickel color centers in ND substrates. Using the confocal microscope, we worked with 

Howard University and successfully helped them 

characterize single photon-emitters in their ND samples. We view this confocal microscope as a strong 

starting point to build the future of quantum information research in ITL.

7. Alan Mink developed hardware (FPGA) and software to support the NIST IMS quantum randomness 

project in the areas of random number generation and 

capturing time tagged Bell test data as well as for 

post-processing of quantum random number generation. He also investigated post-processing (error 

correction and privacy amplification) for Gb/s QKD 

using attached processors (e.g., FPGAs, GPUs, etc.) 

[3, 4] and made contribution to the international effort in the development of QKD standards. 

8. During FY 2014, the Phase 1 (proof of principle) of 

our SBIR to generate narrow band single photon 

pairs using a Bragg-grating enhanced SPDC chip 

with a pi-phase shift was successfully completed. 

Funding for Phase 2 was approved and work on the 

Phase 2 began toward the end of FY 2014. A successful SBIR will provide a convenient and compact 

source of narrow-band single photon pairs that will 

be commercially important in future compact quantum applications. Oliver Slattery leads this effort. 

Future research. In FY 2015, based on the work done 

in the previous year, the team will continue the efforts 

to improve the performance of the photon sources, the 

quantum interfaces and the quantum memory. In the 

coming years, when the performance of these devices 

reaches the necessary level, we will demonstrate a prototype of a quantum repeater. 

[1] Y.-S. Kim, O. Slattery, P. S. Kuo and X. Tang, Two-photon Interference with Continuous-wave Multi-mode 

Coherent Light, Optics Express 22:3 (2014), 3611-3620. 

[2] P. S. Kuo, J. S. Pelc, O. Slattery, L. Ma and X. Tang, Domain-engineered PPLN for Entangled Photon Generation 

and Other Quantum Information Applications, in Proceedings of the SPIE 9136 (2014), 913403. 

[3] A. Mink and A. Nakassis, LDPC Error Correction for 

Gbit/s QKD, in Proceedings of the SPIE: Defense Security & Sensing 9123 (May 2014), 912304-1.

[4] A. Nakassis and A. Mink, Polar Codes in a QKD Environment, in Proceedings of the SPIE: Defense Security & 

Sensing 9123 (May 2014), 912305-1.
Summary of Activities for Fiscal Year 2014 91

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 

Computer Studies (UMIACS); the UMD Departments 

of Physics and Computer Science; and the UMD Applied Mathematics and Statistics, and Scientific 

Computation program with NIST’s Information Technology and Physical Measurement Laboratories.

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 

is 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.

Jordan and Liu were 

co-organizers of a planning 

workshop22 for the new center held on March 31 – April 

1, 2014 in College Park. 

The well-attended event 

featured talks by Andrew 

Childs (University of Waterloo), Seth Lloyd (MIT), 

Scott Aaronson (MIT), 

Daniel Gottesman (Perimeter Institute), Manny Knill 

(NIST), and Nicolas Gisin 

(University of Geneva).

 

22 http://www.nist.gov/itl/math/quics-workshop.cfm

Figure 72. Officials from the participating organizations gather to sign the MOU establishing QuICS. 

Front: Willie May, Acing Director of NIST; Mary Ann Rankin, Senior Vice President and Provost of the 

University of Maryland; Deborah Frinke, Director, NSA Central Security Service. Back: Carl Williams, 

Chief, NIST Quantum Measurements Division; Amitabh Varshney, Director, UMD Institute of Advanced 

Computer Studies (UMIACS); Jayanth Banavar, Dean, UMD College of Computer, Mathematical and 

Natural Sciences; Dianne O’Leary, UMD Dept. of Computer Science and Founding Co-Director of 

QuICS; Jacob Taylor, NIST Physical Measurement Lab and Founding Co-Director of QuICS; PatricknO’Shea, UMD Vice President and Chief Research Officer; Samir Khuller, Chair, UMD Dept. of

Computer Science.
Summary of Activities for Fiscal Year 2014 92

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.

Modeling of Kinetic-based Micro 

Energy Harvesters for Wearable and 

Implantable Sensors

Kamran Sayrafian

Mehdi Dadfarnia (NIST EL)

Antonio Possolo (NIST ITL)

Paul Mitcheson (Imperial College, UK)

See page 24.

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, the challenge of characterizing 

larger and larger networks is only getting harder.

Conventional algorithms for graph visualization 

render such networks as a solid blot of color from which 

is difficult to discern meaningful information. This difficulty is strongly influenced by the presence of highdegree nodes (hubs) which entangle many parts of the 

graph with itself, together with the sheer volume of 

nodes and edges which makes rendering into a reasonable image size for viewing and printing impractical.

An alternate approach is to visualize important network properties, rather than the actual network itself. 

These 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: small connected components of a graph, in the absence of highdegree 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.

The Q-matrix of a network, in its fundamental formation, is a connected component size distribution 

matrix for a series of degree-limited subgraphs of the 

original network (or weakly-connected component for 

Figure 73. Non-trivial components of math.nist.gov web graph, restricted to nodes with combined degree less than or equal to 

25.(math_d4_25.png)
Summary of Activities for Fiscal Year 2014 93

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 individual pages, and edges are directed hyperlinks 

between two web pages. Figure 73, for example, illustrates connected components of the math.nist.gov Web 

graph, where nodes of degree greater than 25 have been 

removed.

The image reveals various structures: e.g., ladders, 

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 rendered by projecting its nonzero values onto the z-axis 

and displaying it as a three-dimensional structure, as 

show in Figure 74.

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 (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 < 60 sec.

This year we created new optimized algorithms in 

compiled C++ that are both efficient in space and computational time, allowing us to compute Q-matrices for 

networks with over 1 billion edges in less than one hour 

on common desktop computers. These large datasets allow us to see finer complexity patterns not present in 

smaller sample sets.

We are also extending research of the Q-matrix theory to generalized vertex orderings beyond that of node 

degree, such as PageRank, eigenvalue centrality, betweeness centrality, and k-core numbers. We are 

exploring alternate metrics for network communities 

(such as the alignment of subgraph S, which compares 

the sparsity of S to the number of its distinct neighbors). Furthermore, we are investigating the use of Qmatrix analysis to specific problems in the area of microbiology (genomic networks) and economics 

(financial market networks).

[1] R. Pozo, Q-Matrix: An Algebraic Formulation for the 

Analysis and Visual Characterization of Network Graphs, 

in review.

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 

Figure 74. Q-matrix plot of math.nist.gov webgraph (29K vertices, 

62K edges) showing the component size distribution of degree-limited subgraphs.
94 NIST Applied and Computational Mathematics Division

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.

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(2nn

O(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. 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] Y. Kemper and I. Beichl, Monte Carlo Methods to Approximate the Chromatic Polynomial, in preparation.

An Improved Feedback Vertex Set 

Heuristic

James M. Shook 

Isabel Beichl

To recover from deadlock it is sometimes necessary to 

end processes so that resources can be made available. 

Deadlock recovery has applications in operating systems, database systems and VLSI chip design. One 

would hope to end the fewest possible processes. To decide which processes to end, it is necessary to 

understand the relationship between processes. This can 

be represented by a directed graph called a dependence 

graph. If the dependence graph has a cycle, then deadlock has occurred and we need to end a process on that 

cycle. A feedback vertex set (FVS) is a set of vertices or 

processes that when removed from the dependence 

graph leave the resulting graph without cycles. Thus, the 

FVS gives the smallest number of processes to end to

remve all deadlocks. Unfortunately, finding the smallest 

FVS has been shown to be NP-hard [2]. Thus, research 

has focused on finding an efficient heuristic for the FVS

problem.

 In [3] the authors presented a method that finds a

FVS, F, with a running time of O(|F| n

2.376), where n is 

the number of nodes in the network and |F| is the size of 

the FVS. Evidence was given that their method was superior to existing heuristics. Relating an observation 

made in [1], to disjoint cycle unions, we designed a 

method that has a running time of O(|F| log(n) n

2

). For 

comparison we tested each algorithm on Erdös-Rényi 

random graphs and random k-regular graphs of various 

orders. Our method found smaller sets than the method 

in [3]. We also found that our method approximated the 

actual size of a minimum FVS well. A detailed analysis 

of our work has been submitted for publication.

[1] I. Beichl and F. Sullivan, Approximating the Permanent 

via Importance Sampling with Application to the Dimer 

Covering Problem, Journal of Computational Physics

149:1 (1999), 128-147.

[2] R. Karp, Reducibility among Combinatorial Problems, in 

Complexity of Computer Computations (R. Miller and J. 

Thatcher, eds.), Plenum Press, 1972, 85-103.

[3] M. Lemaic and E. Speckenmeyer, Markov-Chain-Based 

Heuristics for the Minimum Feedback Vertex Set Problem, Computer Science Technical Report, University of 

Cologne, 2009. 

Extremal Theorems for Degree 

Sequence Packing and the 2-Color 

Discrete Tomography Problem

James Shook

Jennifer Diemunsch (University of Colorado Denver)

Michael J. Ferrara (University of Colorado Denver)

Sogol Jahanbekam (University of Colorado Denver)

Discrete tomography is a form of image processing in 

which discrete objects are reconstructed using data acquired from low-dimensional projections. Discrete 

tomography has uses in medical imaging, electron microscopy, and materials science. In the k-color discrete 

tomography problem the goal is to color 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, which we 

explain below, for degree sequences of k bipartite graphs 

with parts of sizes m and n. 

We approached the problem by proving more general questions in graph packing. A sequence π = (d1, ..., 

dn) is graphic if there is a simple graph G with vertex set 

(v1, ..., vn) such that the degree vi is di. We say that 

graphic sequences π1 = (d1

(1)

, ..., dn

(1)) and π2 = (d1(2)

, ..., 

dn

(2)) pack if there exist edge-disjoint n-vertex graphs G1 

and G2 such that for j {1, 2}, dGj(vi) = di

(j)

, for all ε {1, 
Summary of Activities for Fiscal Year 2014 95

..., n}. We proved several extremal degree sequence 

packing theorems that parallel central results and open 

problems from the graph packing literature. Specifically, the main result of our work implies a degree 

sequence packing analogue to the widely studied 

Bollobás-Eldridge-Catlin graph packing conjecture

found in [1] and, independently, in [2], along with a degree sequence version of the classical graph packing 

theorem of Sauer and Spencer found in [3]. We modified 

our techniques to prove several Sauer-Spencer-type theorems that have direct applications to the 2-color 

discrete tomography problem.

[1] B. Bollobás and S.E. Eldridge, Packings of Graphs and 

Applications to Computational Complexity, Journal of 

Combinatorial Theory Series B 25 (1978), 105-124.

[2] P. Catlin, Embedding Subgraphs and Coloring Graphs 

under Extremal Degree Conditions, Ph.D. Thesis, Ohio 

State University, 1976.

[3] N. Sauer and J. Spencer, Edge Disjoint Placement of 

Graphs, Journal of Combinatorial Theory Series B 25

(1978), 295-302.

Fast Sequential Creation of Random 

Graphs

Brian Cloteaux

 Creating random degree-based graph models has 

become an important first step in creating a model of a 

network. Before about seven years ago, the only way to 

create a random model with a given a degree sequence 

would be to create an instance by the Havel-Hakimi 

algorithm and then do a walk on the Markov chain (MC) 

of edge switches in the graph. This method is fast, but 

little is known about bounds on the mixing time of this 

walk. In general, based on some conjectures made about 

the mixing-time time of these chains, the normal runtime is O(m log n), where n is the number of vertices and 

m is the number of edges. In addition, the algorithm is 

difficult to modify for creating graphs with given 

characteristics.

In 2010 Blitzstein and Diaconis [1] published a 

sequential importance sampling (SIS) method for 

creating random graphs with a given degree distribution. 

This algorithm allows for much more flexibility in the 

characteristics of the random graphs created, but 

unfortunately, the run-time of their method is much 

slower than the MC method. Former NIST NRC 

Postoctoral Associate Lizz Moseman [2] showed that 

the Blitzstein-Diaconis (BD) algorithm run time could 

be reduced from O(mn2) to O(mn), but this still does not 

match the time of the MC algorithm. 

We have examined ways of improving the BD 

algorithm by looking at the structures of edges that must 

be avoided at each step of the BD algorithm. For a given 

degree sequence d, a forced edge is an edge that must 

appear in every realization of d, while a forbidden edge 

is an edge that cannot appear in any realization of d. 

Using these definitions, we can informally describe the 

BD algorithm as randomly choosing edges that are not 

in the forbidden set at each step. We examined the 

structure of these sets of forced and forbidden edges in 

order to speed up checking for them during the BD 

algorithm, and proved several results including showing 

the structure of these forced and forbidden sets. In 

Figure 75, we show the increase in probability for 

finding possible graphical edge choices when we 

account for forbidden and forced edges.

Using these results, we have created two new 

versions of the BD algorithm, whose speeds approach 

that of the MC algorithm. We have also introduced a 

completely new algorithm for the sequential creation of 

graphs. This algorithm differs from BD algorithm 

because it chooses a set of edges for each step, but 

allows for much quicker edge acceptance times. This 

algorithm essentially matches the MC run-time, but still 

allows for the advantages of SIS approaches. 

Anecdotally, we can understand the speed-up of 

these new algorithms from a case-study. Several years 

ago, we created a series of models of the autonomous 

system (AS) topology of the internet using a C++ 

implementation of the original BD code. This code took 

around two hours to create each model. Using the new

BD algorithm, we were able to create instances from the 

same degree sequence in about 16 seconds. In fact, we 

were able to run statistical tests on the algorithm by 

creating over 45,000 random instances with many of 

these instances being larger than the AS topology degree 

sequence. This would have been impossible for the 

original BD algorithm.

Figure 75. The increase in probability for finding possible graphical edge choices when we account for forbidden and forced edges.
96 NIST Applied and Computational Mathematics Division

[1] J. Blitzstein and P. Diaconis, A Sequential Importance 

Sampling Algorithm for Generating Random Graphs with 

Prescribed Degrees, Internet Mathematics 6:4 (2010), 

489.

[2] E. Moseman, Improving the Computational Efficiency of 

the Blitzstein Diaconis Algorithm for Generating 

Random Graphs of Prescribed Degree, unpublished 

manuscript, 2011.

Identifying Important Nodes in a 

Network for Rapid Communication 

Fern Y. Hunt

We are studying the problem of effective communication in a network of nodes that only communicate with 

their neighbors. Given the pattern of communication we 

seek to identify a set of informed nodes of predetermined cardinality that will enable the fastest spread of 

information in the network. One can also seek the solution to a similar problem: find the set of informed nodes 

that will maximize the number of contacted nodes in 

some period of time. The motivation for this research is

the control of large networks when the resources for direct centralized communication are limited. Thus there 

are potential applications, for example, to the design of

sensor networks for the detection of breakdown in energy and water supply systems. There are also

applications to the propagation of influence in social 

networks, as well as the study of gene regulatory networks.

Our mathematical approach to the fastest communication problem is to define a set function related to the 

time it takes for uninformed nodes to receive information from a selected set of informed nodes. The 

function becomes the objective function which must be 

minimized over the class of all subsets of nodes of maximum size K. This is a classic problem in combinatorial 

optimization and early, significant work by Nemhauser 

et al. [1], established important results when the objective function is a bounded submodular (or as in our case 

supermodular) function. Their work, and the extensive 

research that followed, showed that the simple intuitive 

approach of constructing an optimal K element set by 

first identifying the best one element set and then successively adding an element that creates the best new set 

containing its predecessor, results in an approximation 

to the optimization problem that is guaranteed to be 

within 1-1/e of optimal. Nevertheless the problem is NPhard and the preponderance of current theoretical research shows that the ratio cannot be improved by much 

given the problem as stated. 

In the past year we continued our reformulation of 

the problem so that information about the topology of 

the network graph and the structure of the class of optimal sets is employed in its solution. Originally the 

solution was required to be a subset of cardinality K or 

less (that is, an element of a matroid). In our approach 

sets are constrained to lie in a much smaller class of optimal and “nearly” optimal subsets (see [2] for details). 

This class is closed under addition of elements (as occurs in the greedy algorithm), deletion of elements (as in 

the backward greedy algorithm) and exchange of elements in sets of equal cardinality (as in a local search). 

We also stated sufficient conditions on the network 

graph for the existence of a greedoid containing optimal 

and near optimal sets—a more general set system than 

the original matroid and a concept better suited to the 

order dependence that we believe is intrinsic to the problem. Within this framework we are able to study 

different schemes for the stepwise construction of approximations. In addition to work on the greedoid, we 

also implemented an approximation method based on 

sets in the greedoid that are subsets of a vertex cover of 

the network graph. Our new method is based on greedy 

extensions of the smallest sized optimal and “nearly”

optimal sets in a greedoid. Empirically we found the approximations to be better than the (1-1/e) bound of 

Nemhauser et al. and others, and often are an exact solution. When the greedy algorithm approximation is 

itself the exact solution, it is a special case of our greedy 

extension approach.

Pre-processing is needed to compute the optimal 

and “near” optimal subsets in the greedoid. If N is the 

number of nodes, and m is the size of the smallest optimal or near optimal set then we conjecture that the 

method has complexity Ο(N

m) ∙ poly(N) where 

poly(N) is polynomial in N. The next question, of 

course, is why and under what conditions do these methods work? Intuitively, restricting the search space to 

optimal and “nearly” optimal sets excludes poorly performing sets, including bad starting points for a stepwise 

algorithm. The search for a deeper and more rigorous 

understanding is currently underway. Recent research 

advances by Filmus and Ward have been made using the 

concept of curvature for submodular and supermodular 

functions in the matroid case [3]. We are currently investigating curvature in our setting with a view toward 

obtaining bounds on the performance of our proposed 

method.

[1] G. Nemhauser, L. A. Wolsey and M. L. Fisher, An Analysis of Approximations for Maximizing Submodular Set 

Function – I, Mathematical Programming 14 (1978), 

553-574.

[2] F. Y. Hunt, The Structure of Optimal and Near Optimal 

Target Sets in Consensus Models, NIST Special Publication 500-303, August 2014.

[3] Y. Filmus and J. Ward, Tight Bounds for Submodular and 

Supermodular Functions with Bounded Curvature, 

arXiv:1204.4526.
Summary of Activities for Fiscal Year 2014 97

Measurement Science for Systemic 

Risks in Critical Infrastructures 

Vladimir Marbukh

Technological advances combined with pressures of 

economic globalization have produced highly interconnected national and world-wide infrastructures, which 

have become essential for U.S. industrial competitiveness and economic security. In communication 

networks, cloud computing architecture, power grid, financial networks, supply chains, etc., interconnectivity 

makes resource sharing possible, creating load balancing capabilities at the cost of systemic risks of cascading 

failures/overload, virus propagation, and misuse of the 

additional resource access capabilities by strategic or 

malicious participants. We have already experienced 

significant strategic and economic losses due to these 

negative consequences. Interconnectivity, and the resulting problems, will grow with time unless serious 

measures are taken to mitigate the relevant risks

Paper [1] attempts to quantify systemic risk of the 

cloud computing infrastructure. The economic and convenience advantages of the shared cloud computing 

infrastructure as compared to the conventional model of 

owning computer resources are unquestionable. Among 

the economic advantages are elimination of the fixed 

cost and reduction of the marginal cost for users of cloud 

computing infrastructure due to the benefits of dynamic 

load balancing and the economy of scale. Results in [1] 

indicate that in a practically relevant parameter region, 

the benefits of dynamic load balancing in the “normal 

operating regime” come with risks of the system abruptly transitioning to a “persistently congested mode” 

through the process of cascading overload.

Paper [1] can be viewed as a first step in the direction of a paradigm shift in cloud design and operation: 

from maximizing economic benefits to identifying and 

managing the relevant risk/benefit tradeoffs. In particular, [1] demonstrates that economic pressures push the 

system to the stability boundary of the normal operating 

regime, making the tradeoff between “normal system 

performance” and the systemic risk of transitioning to a 

congested regime more acute. In [1] we also suggest

using the Perron-Frobenius eigenvalue of the “reduced” 

system performance model as a measure of the systemic 

risk of cascading overload. Applicability of the PerronFrobenius theory in systems with dynamic resource 

sharing is due to the positive feedback in the system 

component overload, which can spill over to the “neighboring” components.

Presentation [2] discussed a general form of systemic risk of cascading overload due to a “non-native” 

service being less efficient than the “native” service, 

e.g., as a result of an additional cost of accessing distant 

resources. Consistent with [1], analysis [2] indicates 

that the systemic risk/performance tradeoff may be a result of coexistence of metastable, i.e., persistent, normal 

and congested system states: resource sharing is beneficial or harmful depending on the system being in the 

normal or congested metastable state. Moreover, peak 

system performance in the normal metastable state is 

achieved close to the stability boundary of the state.

Some of these findings are illustrated in Figure 76, 

which sketches a portion of system lost revenue L as a 

function of the level of resource sharing α.

 The optimal level of resource sharing α = α

opt is 

typically unacceptably close to the stability boundary α

= α

* of the normal metastable state represented by curve 

A0A*A

*

. The systemic risk of a discontinuous phase transition A

*B*

to the “congested” metastable state, 

represented by curve B*B

*E, can be reduced by lowering 

α below α

opt at the cost of sacrificing “normal” system 

performance.

Managing this systemic risk/performance tradeoff 

is a challenging problem due to the difficulty of realtime monitoring of the system stability margin and the 

tendency of strategic system components to drive the 

system beyond the stability boundary due to positive externalities. Since systemic risk is an inherently 

macroscopic phenomenon, the proposed approach is 

based on the reduced, i.e., macroscopic, system description in the subspace of the eigenvectors corresponding 

to the largest eigenvalues of the linearized system dynamic. In [3] we suggest that a similar systemic 

risk/performance tradeoff may be essential in softwaredefined networking infrastructures.

Presentations [4-5] discuss the risk of cascading 

failures described by the Susceptible-Infected-Susceptible (SIS) model. Presentation [4] suggests that the 

recently discovered phenomenon of eigenvector centrality localization may be used for characterization of the 

hierarchy of important infection spreaders in large-scale 

networks. This characterization may help with prediction and mitigation of the impact of persistent infections 

through regulations or incentives. In [5] we propose a 

tractable model describing the interplay between infection propagation on the network and the evolution of the 

network topology. The model assumes that infection 

Figure 76. Portion of lost revenue vs. level of resource sharing. 0

1 A0 E



*

*



opt  1 A*

* A B*

* B

L
98 NIST Applied and Computational Mathematics Division

propagation follows a Susceptible-Infected-Susceptible 

(SIS) process with controlled node recovery rates and 

network topology evolution follows a preferential rewiring process.

[1] V. Marbukh, On Systemic Risk in the Cloud Computing 

Model, in Proceedings of the 26th International 

Teletraffic Congress (ITC 26), Karlskrona, Sweden, 

2014.

[2] V. Marbukh, “Systemic Risk/Benefits of Interconnectivity due to Metastability,” NetSci 2014, 

Berkeley, CA, 2014.

[3] V. Marbukh, “SDN: Systemic Risks due to Dynamic 

Load Balancing,” Software Defined Networking 

Research Group, Internet Research Task Force, IETF 91, 

Honolulu, HI, 2014.

[4] V. Marbukh, “Eigenvector Centrality Localization and 

Hierarchy of Important Spreaders in Large-Scale 

Networks,” NetSci 2014, Berkeley, CA, 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 2014.

Security of Complex, Interdependent 

Systems

Assane Gueye (University of Maryland)

Richard J. La (University of Maryland)

Understanding the security of large-scale, complex 

interconnected networks and systems has emerged as 

one of the key challenges information system engineers 

face today. Studying the system-level security of such 

networks or systems is hampered by the fact that security measures adopted by various agents or organizations 

or lack thereof produce network externalities on other 

organizations, resulting in so-called interdependent security (IDS). 

In the past, there has been much research in studying how the infection of a few agents (e.g., disease 

outbreaks or epidemics and spread of computer viruses 

or malware) may spread to a large number of other 

agents through networks (e.g., computer networks or social networks). Most existing studies focus on scenarios 

where the agents are passive in that they do not take proactive measures to protect themselves based on 

perceived risks and threats. In many scenarios of interest, e.g., cybersecurity and disease outbreaks, however, 

agents can employ various measures to lower the likelihood of getting infected, often by their neighbors. 

We take a first step towards correcting this current 

state of affairs and examine the scenarios where the 

nodes are strategic entities that are interested in optimizing their own objectives. We model the interdependence

in security among agents, which is brought on by network externalities, using a dependency graph, in which 

the nodes/vertices are the organizations and an edge between two vertices indicates a dependence/relation 

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 the 

resulting overall network-level security. 

We focus on two different scenarios. In the first scenario [1, 2], each node has three available choices – (i) 

protect itself, (ii) purchase insurance for informational 

or financial losses, or (iii) take no protective measure. 

Due to the network externalities or interdependence of 

security, the choices made by the nodes are coupled. Using a population game model, we investigate how 

network properties, e.g., node degree distributions, and 

other system parameters, e.g., infection propagation 

rate, shape the choices of nodes and ensuing loss of efficiency (measured using the price of anarchy (PoA)) at 

Nash equilibria of population games. 

In the second scenario [3], we generalize the previous model and allow nodes to choose from M (M>1) 

different protection levels with increasing security investment costs. In addition, they can also purchase 

insurance and the insurance premium depends on the 

protection level of the insured. Finally, the insurers may 

require a certain minimum level of protection before 

agreeing to insure organizations. We extend the key 

findings we obtained using the first model to these more 

general cases. 

One of our key findings is that, as the weighted node 

degree distribution (where the weights are given by node 

degrees) becomes stochastically larger, (a) a node with 

a fixed degree tends to invest less in security measures, 

(b) somewhat surprisingly, the risk or threat seen from a 

neighbor diminishes, and (c) the probability that the infection of a few nodes triggers a cascade of infection, 

i.e., a large number of nodes become infected, climbs. 

These findings suggest that when the weighted node degree distribution is larger, while a node with a fixed 

degree may feel that the overall network-level security 

is better from finding (b), the network-level security 

measured by the probability of global cascade in fact deteriorates from finding (c). Furthermore, the PoA tends 

to increase with the weighted node degree distribution, 

indicating that the overall network-level security suffers 

in comparison to system optimum.

We are currently investigating how other network 

properties, such as network assortativity, affect the network-level security when agents are strategic [4]. Our 

preliminary results suggest that as the network becomes 

more assortative, i.e., nodes tend to be connected to 

other nodes with similar degrees, the overall security investments fall and the network-level security degrades. 

This observation reveals that it is likely more challenging to stop an epidemic in a community, whereas 
Summary of Activities for Fiscal Year 2014 99

preventing a wide spread of computer malwares and viruses may be easier than previously thought.

[1] R. J. La, Role of Network Topology in Cybersecurity, in 

Proceedings of IEEE Conference on Decision and Control (CDC), Los Angeles, CA, December 2014. 

[2] R. J. La, Interdependent Security with Strategic Agents 

and Global Cascades, IEEE/ACM Transactions on Networking, to appear. 

[3] R. J. La, Effects of Degree Distributions on Network Security—Population Game Model, in review. 

[4] A. Gueye and R. J. La, “Influence of Assortativity on Network Security,” Poster, NetSci Workshop, Berkeley, CA, 

June 2014. 

This research was supported by NIST Cooperative 

Agreements 70NANB13H012 and 70NANB14H015.

Graph Theoretic Applications to 

Network Security and Security 

Metrics

Assane Gueye (University of Maryland)

Richard J. La (University of Maryland)

Peter Mell (NIST ITL)

Rich Harang (Army Research Laboratory)

In this project, we first studied the strength of 

interconnectivity between countries in the Internet, 

using the connectivity among autonomous domains 

(ASs) obtained by analysis of data available from 

(CAIDA) over several years[1]. Secondly, we examined 

how difficult it is to (i) stop the flow of information 

between two countries, (ii) isolate a given set of 

countries, or (iii) break up the Internet into a group of 

(disconnected) components. 

To answer these questions, we created an 

interconnectivity map of the worldwide Internet routing 

infrastructure at a country level on the basis of AS-level 

information after filtering the CAIDA data sets. We first 

demonstrated that the interconnectivity among countries 

has increased over the years during which measurements 

had been taken. Then, we examined how groups of 

countries may use the ASs under their control/regulation 

to filter out the traffic of other countries (or to block 

entire routes). Our analysis indicates that the ability of 

countries to disrupt the connectivity between countries 

has diminished significantly from 2008 to 2013. 

However, we showed that the majority of the gains in 

robustness, i.e., increase in connectivity, goes to 

countries that had already displayed significant 

robustness to the types of attacks that we considered. 

The countries that had displayed higher vulnerability to 

such attacks did not experience a significant 

improvement in resilience over the same time period 

considered in the analysis.

In the second part of the project, we investigated the 

problem of creating defensive choke points within 

networks, and defining metrics for network resilience 

against attack propagation. Securely configured IPv6 

networks can be made resistant to network scanning and 

other forms of target acquisition, forcing attackers to 

propagate through a network only by following existing 

benign communication paths. If heightened security 

measures are taken to protect a select group of hosts, the 

layer 4 network communication graph (not the physical 

or logical network graph) can be broken into small 

isolated clusters connected by a few highly protected 

“checkpoints’. Attackers attempting to propagate 

through the network will then be required to penetrate 

one or more checkpoints or else be limited to a small set

of targets. The checkpoints increase the chance of 

detection and/or limit an attacker’s ability to propagate 

through the network (depending upon the nature of the 

heightened security capability). 

Optimal placement of checkpoints requires solving 

the NP-complete vertex separator problem, and so we 

approximated optimal solutions via a suite of heuristics. 

We empirically tested our approach and algorithms on 

data from an operational network with over 15,509 

nodes and discovered that heightened security measures 

are only needed on 100 nodes (< 1 %) to restrict attacker 

propagation to no more than 15 % of the network. This 

enables a novel defense-in-depth layer that 

complements traditional security approaches. It can be 

enhanced with a moving defense model where the 

special security measures migrate between nodes 

following locally optimal configurations, causing 

uncertainty to the attackers as to where the checkpoints 

are deployed, and enabling defensive agility as network 

communication graphs change over time.

We are currently investigating how one can take 

into account the underlying communication graph 

properties in order to design more efficient algorithms 

for identifying effective checkpoints. In particular, we 

are interested in leveraging the existing literature on 

network science and epidemiology.

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

Internet to Colluding Country Induced Connectivity 

Disruptions, in review.

[2] Assane Gueye, P. Mell, R. Harang and R. J. La, Moving 

Target Defenses with Security Checkpoints in IPv6 

Networks, in preparation.

This research was supported by NIST Cooperative 

Agreements 70NANB13H012 and 70NANB14H015.
100 NIST Applied and Computational Mathematics Division

Uncoordinated Scheduling Strategies 

for Interference Mitigation across 

Body Area Networks

Martina Barbi (University of Bologna)

Kamran Sayrafian

Vladimir Marbukh

John Hagedorn

Judith Terrill

A Body Area Network (BAN) is a radio standard for 

wireless connectivity of wearable and implantable sensor nodes that are located inside or in proximity to the 

human body. Many applications of BANs (e.g. physiological monitoring) require reliable communication of 

information between the sensor nodes and their controller. As there are currently no coordinating mechanisms 

among multiple co-located BANs, interference caused 

by co-channel transmission in adjacent BANs could impact the reliability and in general quality of the service 

experienced by a receiver node within an individual 

BAN. Advanced signal processing using interference 

cancellation techniques has been proposed to minimize 

the impact of this interference. However, there are two 

main problems with such techniques especially when it 

comes to their application in BAN. First is the high complexity of the receiver which makes the implementation 

of interference cancellation impractical unless the number of nodes is very small. Complexity is especially a 

critical issue for nodes in body area networks. As they 

mainly rely on battery power, prolonging the lifetime of 

these nodes is of prime importance. 

The second problem is that some interference cancellation schemes require knowledge of the channel 

condition (such as attenuation, phase, and delay) between each of the interferers and the receiver. Obtaining 

accurate estimates of the channel condition is extremely 

difficult for body area networks. Transmission power 

control has also been considered as an alternative for individual BANs to maintain reliable operation even in 

high interference environments. However, the complexity of the BAN channel environment and other stability 

issues indicate that power control alone may not be able 

to achieve an acceptable system performance.

Due to the possible inefficiency of power control 

and the stated problems with interference cancellation, 

interference mitigation techniques can be an attractive 

alternative, particularly in an environment with high interference level. These techniques can be classified into 

two groups: un-coordinated and coordinated mitigation. 

The coordinated schemes will require appropriate protocols for inter-BAN information exchange, and are 

envisioned to be more sophisticated. However, they 

might result in higher overall performance compared to 

uncoordinated schemes. The uncoordinated schemes require no inter-BAN communication and could result in

simple implementation in the current IEEE802.15.6 international standard in BAN. Link layer adaptation is an 

example of an uncoordinated approach that can be used 

as an interference mitigation technique. Although simple to implement, the trade-off for acquiring reliable 

simultaneous transmission in multiple BAN scenarios is 

lower transmission rates.

In this project, we propose smart scheduling algorithms (i.e., slot assignment) as another alternative to 

mitigate inter-BAN interference. Assuming a TDMAbased MAC, the idea is to distribute simultaneous (i.e.,

colliding) multi-BAN transmissions across several time 

slots without any explicit coordination across interfering 

BANs. We assume that each receiver node of a BAN can 

measure the total interference that is being experienced

at each time slot. The decision of which time slot to use 

Figure 77. Histogram of the experienced SIR for the random 

scenario.

Figure 78. CDF of the experienced SIR.
Summary of Activities for Fiscal Year 2014 101

in the next transmission frame, is the key to avoid potential interference by other BANs. Taking advantage of 

possible correlation in the propagation channel, multiple 

BANs can participate in judiciously selecting appropriate slot assignment (i.e., a transmission schedule) in 

consecutive frames in order to avoid time-slots with 

high interference. This setting matches a game theory 

framework as multiple BANs are competing with each 

other to find the best transmission slot assignment that 

incurs the lowest interference for their target receiver. 

We have proposed two simple algorithms, namely 

Random Assignment and Minimum Interference Allocation (MIA) to achieve the above objective. Details of 

these algorithms can be found in [1, 2, 3]. Figure 77

shows the resulting histogram of the Signal-to-Interference Ratios (SIR) experienced by the nodes in a system 

comprised of eight BANs each having three sensors. The 

improvement in the experienced SIRs is clearly visible 

under MIA or Random assignments. The platform that 

has been used to obtain these results has been described 

in [4]. Figure 77 shows results for both tangentially and 

normally polarized antennas used by the transmitting 

nodes. The eight BANs in this scenario are assumed to 

be moving randomly in an 8×8 m2room.

Figure 78 displays the cumulative distribution functions (CDF) of the experienced SIR for the above 

scenario. These graphs show the improvement in the 

system performance in a more tangible way. If the horizontal access is perceived as minimum required SIR, 

then the vertical access represents the link outage probability. The MIA algorithm reduces the outage 

probability by intelligently distributing and re-allocating 

simultaneous and interfering transmissions in non- or 

less-interfering time slots.

The results of our proposed uncoordinated slot assignment strategies show the performance improvement 

in mitigating cross-interference among uncoordinated 

BANs. Although the current version of the BAN radio 

interface standard (i.e., IEEE802.15.6) does not have 

any provision to support inter-BAN coordination, it is 

conceivable that any coordination might result in better 

performance; of course, as a trade-off with more complexity. More detailed studies and experiments are 

needed to determine the feasibility and effectiveness of 

each strategy in mitigating potential interference. We 

also plan to continue this study for other access protocols (e.g., CSMA) as well.

[1] V. Marbukh, K. Sayrafian and M. Alasti, Link-layer Adaptation in Body Area Networks: Balancing Reliability

and Longevity, in Proceedings the 24th Annual IEEE International Symposium on Personal Indoor and Mobile

Radio Communications (IEEE PIMRC 2013), London,

UK, Sept. 2-5, 2013.

[2] V. Marbukh, K. Sayrafian, M. Barbi and M. Alasti, InterBAN Interference Mitigation: A Correlated Equilibrium 

Perspective; in Proceedings of 11th International Conference on Wearable Micro and Nano Technologies for 

Personalized Health (pHealth 2014), Vienna, Austria, 

June 11-13, 2014.

[3] M. Alasti, M. Barbi and K. Sayrafian, Uncoordinated 

Strategies for Inter-BAN Interference Mitigation; in Proceedings of the IEEE 25th Annual International 

Symposium on Personal, Indoor and Mobile Radio 

Communications (PIMRC 2014), Washington D.C., 

USA, Sept. 205, 2014

[4] 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 Info-communications (IEEE 

CogInfocom 2013), Budapest, Hungary, Dec. 2-5, 2013.

Combinatorial Testing

Raghu Kacker

D. Richard Kuhn (NIST ITL)

Yu Lei (University of Texas at Arlington)

James Lawrence

Jose Torres-Jimenez (CINVESTAV, MExico)

Combinatorial testing (CT) is an approach to detect 

combinatorial interaction faults, which may cause a software-system to fail when certain values of some factors 

occur together. Combinatorial testing is based on the insight, referred to as the interaction rule, that while the 

behavior of a software-system may be affected by a 

large number of factors, only a few factors are involved 

in a failure-inducing fault. Actual faults show that most 

involve 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 

leadership in advancing the technology from pair-wise 

to higher strength testing, making research tools and 

techniques favailable to US industry, and helping to promote their effective use. Many critical system failures in 

recent times have been traced to interaction faults in the 

underlying software. CT is a versatile and broadly applicable methodology that is helping to reduce testing costs 

in software-based systems for science, commerce, defense and security, and electronic medical systems, and 

is increasingly used in hardware testing as well. CT is 

now included in software engineering courses taught in 

more than twelve U.S. universities. A NIST special publication on CT [1] has been downloaded more than 

28,000 times. 

Test suites for CT typically involve factors with 

varying (mixed) numbers of test settings and often involve complex constraints among factors and their test 

settings. ACTS is a NIST-UTA (University of Texas at 

Arlington) research tool to generate high strength test 

suites for CT. A unique feature of ACTS is support of 

constraints among factor and test settings. The version 

2.91 of ACTS incorporates a new algorithm which significantly improves performance of constraint handling. 
102 NIST Applied and Computational Mathematics Division

We have filled over 1800 requests for ACTS.

CCM is a new research tool (developed jointly with 

Itzel Dominguez-Mendoza of the Center for Metrology 

of Mexico, CENAM) to determine combinatorial coverage of a test suite not developed from a CT viewpoint. 

The latest version of CCM supports constraints and has 

a greatly improved graphical depiction of combinatorial 

coverage. A parallel processing version of CCM is also 

available. Combinatorial deficiency of a test suite can be

remedied by additional tests so CCM can help expand a 

test suite to satisfy stated combinatorial requirements.

ITL staff members co-organized the 3rd International Workshop on Combinatorial Testing (IWCT), 

which was held in conjunction with the 7th IEEE International Conference of Software Testing, Verification 

and Validation (ICST) in Cleveland, Ohio (March 31-

April 4, 2014) to bring together researchers, developers, 

users, and practitioners to exchange ideas and experiences with CT methods and tools. The 2014 workshop 

consisted of twelve papers, one keynote address, two 

poster presentations, and thirty participants. The fourth 

IWCT is scheduled for April 13, 2015 in Graz, Austria.

With the sponsorship of NIST, a group of four students from the Carnegie Mellon University Master of 

Software Engineering program developed a proof-ofconcept tool that integrates the power of CT with the advantages of model-driven testing and automatic test 

execution. The input to the tool is a graphical representation of the input domain of the artifact under test 

(AUT) called a Classification Tree (developed by 

Grimm and Grochtmann in 1993). Once created, the 

model is parsed and passed to CitLab that uses ACTS to 

generate the combinatorial test matrix. The test matrix 

may then be manually complemented with the expected 

result for each of the test vectors in the matrix to become 

a test suite. Alternatively, automated generation of expected results (through model checking or simulation) 

for each test vector can be used, with results integrated 

into the test tool through external scripts. The test suite 

is then fed to a Junit parameterized test that executes the 

AUT and records the pass/fail result for each test case.

Software product line (SPL) is an emerging paradigm for building a family of software systems that 

share similar features. The new algorithm developed by 

the NIST CT team for handling constraints for SPL is 

based on the notion of minimum invalid tuples. We 

compared our algorithm to an existing algorithm called 

ICPL, which is considered by far the best. The results 

are very encouraging. We show that our algorithm performed significantly better on the 15 largest feature 

models in a benchmark repository, both in terms of test 

set size and execution time. We incorporated the new 

algorithm into ACTS. A paper on this work was presented at the 2014 IEEE High Assurance System 

Engineering Conference [3].

 

23 http://www.tamps.cinvestav.mx/~jtj/authentication.php

Fault localization is one of the most difficult and 

time-consuming tasks during software development. We 

developed a spectrum-based approach that actually 

identifies faults inside source code by leveraging the notion of inducing combination. In particular, our 

approach generates a small group of tests from an inducing combination, such that the execution traces of these 

tests can be analyzed to quickly locate the faults. A paper was presented at ISSRE 2013 [4]. After the 

publication, we further refined this approach and integrated it with our earlier work on identifying inducing 

combinations. We conducted additional experiments to 

evaluate the effectiveness of the integrated approach. In 

particular, we made an experimental comparison with 

two state-of-the-art spectrum-based fault approaches. A 

journal paper is being prepared on the integrated approach and the new experimental results.

Test suites for CT are based on mathematical objects called covering arrays. Dr. Jose Torres-Jimenez 

(from the Mexican National Polytechnic Institute Center 

for Research and Advanced Studies, CINVESTAV) has 

joined the NIST CT team. He has developed an extensive library of covering arrays, called the CINVESTAV 

Covering Array Repository23 (CCAR), of the smallest 

known number of test. This will further improve the 

generation test suites for combinatorial testing.

The NIST CT team has made presentations for three 

years at the annual NASA Independent Verification and 

Validation (NASA IV&V) Workshops. The title of the 

2014 presentation was “Using combinatorial methods to 

determine test set size.” NIST is working with the Johns 

Hopkins University Applied Physics Laboratory on a pilot project involving use of a research tool jointly 

developed by NIST and the U.S. Marine Corps for fault 

location in an area of defense and security. 

[1] D. R. Kuhn, R.N. Kacker and Y. Lei, Practical Combinatorial Testing, NIST Special Publication 800-142, 2010.

[2] L. Ghandehari, J. Czerwonka, Y. Lei, S. Shafiee, R. 

Kacker and D. R. Kuhn, An Empirical Comparison of 

Combinatorial and Random Testing, in Proceedings of 

3rd International Workshop on Combinatorial Testing (in 

conjunction with 7th IEEE International Conference on 

Software Testing, Verification and Validation), April 

2014.

[3] L. Yu, F. Duan, Y. Lei, R. N. Kacker and D. R. Kuhn, 

Combinatorial Test Generation for Software Product 

Lines using Minimum Invalid Tuples, in Proceedings of 

15th IEEE International Symposium on High Assurance 

System Engineering (HASE), January 2014, 65-72. 

[4] L. Ghandehari, Y. Lei, D. Kung, R. N. Kacker, D. R. 

Kuhn, Fault Localization Based on Failure-Inducing 

Combinations, in Proceedings of 24th IEEE International 

Symposium on Software Reliability Engineering (ISSRE), 

November 2013, 168-177.
Summary of Activities for Fiscal Year 2014 103

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.

DLMF Standard Reference Tables 

on Demand

Bonita Saunders

Bruce Miller

Marjorie McClain

Daniel Lozier

Andrew Dienstfrey

Chris Schanzle

Annie Cuyt (University of Antwerp)

Stefan Becuwe (University of Antwerp)

Franky Backeljauw (University of Antwerp)

See page 38.

Digital Library of Mathematical 

Functions

Daniel W. Lozier 

Barry I. Schneider

Ronald F. Boisvert 

Bruce R. Miller 

Bonita V. Saunders 

Marjorie A. McClain 

Howard S. Cohl 

Charles W. Clark (NIST PML) 

Brian Antonishek (NIST ITL)

Adri B. Olde Daalhuis (University of Edinburgh)

http://dlmf.nist.gov/

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 Digital Library of Mathematical Functions (DLMF) 

together with the accompanying book, NIST Handbook 

of Mathematical Functions [2], published by Cambridge 

University Press 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 improving 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-todate list of references. The website covers everything in 

the handbook and much more: additional formulas and 

graphics, interactive search, live zooming and rotation 

of 3D graphs, internal links to symbol definitions and 

cross-references, and external links to online references 

and sources of software.

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, citations to the DLMF 

are steadily growing. Almost 13 % of all of the citations 

are now to the DLMF as compared to 8 % in 2012. This 

is a healthy trend. See Figure 79.

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 process at NIST include 
104 NIST Applied and Computational Mathematics Division

DLMF Tables [3], an on-demand table generation web 

service for special functions (see page 38), and the Digital Repository of Mathematical Formulae (DRMF) [4, 

5], a community-based context-free compendium of 

mathematical formulas and associated mathematical 

data (see page 107).

During the period covered by this report, there have 

been a number of changes in the project’s management 

structure. The Editorial Board was expanded to include 

Bruce R. Miller as Information Technology Editor, 

Bonita V. Saunders as Visualization Editor and Barry I. 

Schneider as Associate General Editor. These changes 

followed after the death of Frank W. J. Olver, the Editor 

in Chief of the DLMF and the retirement of Daniel W. 

Lozier. Lozier continues to remain active in the DLMF 

as General Editor on a part-time basis.

Now that the set of editors has been expanded, and 

in expectation of future changes in the leadership of the 

project, work to strengthen the rudimentary system currently in use for logging, resolving, archiving and 

otherwise managing feedback from users and between 

the editors is underway. 

To summarize the year’s technical accomplishments, there have been three updates of the DLMF 

during the period of the report. Version 1.0.7 significantly enhanced the accessibility, portability and 

usability of the DLMF. The default document format is 

now HTML5, which includes MathML, providing better 

accessibility and display of mathematics. All interactive 

3D graphics have been recast using WebGL and 

X3DOM, which is now the default format. This improves portability and performance; it is now possible to 

interactively rotate, scale and explore function surfaces 

without downloading a special plugin. (See the next article for further details.) In Version 1.0.8, there were a 

number of mathematical corrections and the characters 

previously used for exponential e, imaginary i and differential d, were changed from special Unicode 

characters, not always available locally for use by 

browsers, to normal characters. In addition, some minor 

changes to page layouts were implemented. In Version 

1.0.9, a few errors caught by readers were corrected, improvements in notation were made, and additional 

citations and clarifications were incorporated. 

Future developments will continue with periodic releases correcting errors and making appropriate changes 

in current mathematical content. There is also likely to 

be a second edition of the DLMF containing some new 

chapters at some point in the next few years. 

[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.

[3] D. Lozier, “Outgrowths of the Digital Library of Mathematical Functions Project, Part I: DLMF Standard 

Reference Tables,” Challenges in 21st Century Experimental Mathematical Computation, Institute for 

Computational and Experimental Research in Mathematics (ICERM), Providence, RI, July, 2014.

[4] 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,” Challenges in 21st Century Experimental Mathematical Computation, Institute for 

Computational and Experimental Research in Mathematics, Providence, RI, July, 2014.

[5] 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, 

Proceedings of the Conferences on Intelligent Computer 

Mathematics 2014, Coimbra, Portugal, July 7-11, 2014, 

(S. M. Watt, J. H. Davenport, A. P. Sexton, P. Sojka and 

J. Urban, eds.), Springer, 419-422.

Visualization of Complex Functions 

Data 

Bonita Saunders

Brian Antonishek (NIST ITL)

Qiming Wang

Bruce Miller

Sandy Ressler

Complex function data visualization can be a powerful 

tool for researchers studying mathematical or physical 

phenomena, but accessibility problems can severely 

limit its usefulness. The original 3D visualizations in 

the NIST Digital Library of Mathematical Functions 

(DLMF) were rendered using VRML and X3D, common technologies for viewing 3D web graphics that 

require users to download a special plugin. This was 

inconvenient not only for users, but also for maintainers 

Figure 79. Recent citation counts for the 1964 NBS handbook (blue) 

and the 2010 NIST Handbook (red). Citations to the classic NBS 

handbook still far outpace citations to the newer edition, 2460 vs. 

311 in 2013, but citations to the latter are steadily growing.
Summary of Activities for Fiscal Year 2014 105

since updates of the plugin, web browser, and even the 

operating system could affect the quality of the graphics 

display. To remedy this problem, we embarked on an 

extensive effort to convert the DLMF 3D graphics files 

to WebGL. 

WebGL is a JavaScript API (application programming interface) for rendering 3D graphics in a web 

browser without a plugin. We based our WebGL code 

on the X3DOM framework which allowed us to build 

our WebGL application around X3D, an XML based 

graphics code. While we never found a VRML/X3D 

plugin that would successfully render our complex visualizations in Linux, our WebGL visualizations are 

visible on Windows, Mac, and Linux platforms in any 

WebGL enabled internet browser. Our conversion work 

paralleled the development of WebGL. When we began 

looking at the feasibility of the conversion more than

two years ago, only trial versions of WebGL enabled 

browsers were available. Today, most common browsers, including the latest versions (11+) of Internet 

Explorer, can render WebGL graphics. WebGL content 

can even be rendered on many mobile devices. Nevertheless, since initial tests and research indicated that 

there were some problems with Microsoft’s Internet Explorer implementation of WebGL, we decided to 

continue offering VRML/X3D display options to users 

for now. This also allows us to accommodate users who

may prefer the VRML/X3D renderings.

The new WebGL visualizations were released in 

version 1.0.7 of the DLMF in March 2014. Figure 80

shows a graph of Jacobian elliptic function sn(x,k) imbedded in a DLMF web page. WebGL color maps are 

more vibrant, cutting plane curves clearer, and the interactive movement of surfaces faster and smoother. We 

did notice that WebGL is more particular about the quality of the underlying computational grid. A few color 

Figure 80. DLMF webpage with embedded visualization of Jacobian elliptic function sn(x,k).
106 NIST Applied and Computational Mathematics Division

map anomalies not seen in the VRML/X3D visualizations were traced to slight overlaps of grid lines. We 

regenerated several grids and boundary contours, greatly 

improving surface color maps and clipping in some 

WebGL visualizations. 

We received very positive feedback after publicizing the new visualizations at various venues and 

websites, including the DLMF website, X3DOM site 

[4], and at several conferences and workshops [1-3]. Future work will concentrate on the reduction of graphics 

file sizes using adaptive grid generation, implementation 

of a continuous surface spin option, development of an 

accurate zoom, and looking at 2D visualization enhancements.

[1] B. Saunders, Q. Wang and B. Antonishek, Adaptive 

Composite B-Spline Grid Generation for Interactive 3D 

Visualizations, in Proceedings of MASCOT/ISGG 2012, 

Las Palmas de Gran Canaria, Spain, October 22-26, 2012, 

IMACS Series in Computational and Applied Mathematics 18 (2014), 241-250.

[2] B. Antonishek, “Look Ma—no Plug-in! (DLMF’s new 

WebGL 3D Figures),” Web3D 2014, 19th International 

Conference on 3D Web Technology, Vancouver, Canada, 

August 10, 2014.

[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] S. Ressler, NIST/DLMF uses X3DOM, 

http://www.X3DOM.org/?page_id=2429.

Mathematical Knowledge 

Management

Bruce Miller

Deyan Ginev (Jacobs University, Germany)

As web technologies continue to develop, and as the 

Digital Library of Mathematical Functions (DLMF)

continues to be corrected and improved, so too must the

Mathematical Knowledge Management (MKM) technologies we originally developed for DLMF.

This year has seen the continued development of 

LaTeXML, the TeX to XML to HTML converter used 

by the DLMF, with a major release last spring, and a 

minor release by the time you read this. Along with bug 

fixes, increased portability, general improvements to

performance, fidelity and styling, the coverage of LaTeX idioms and packages has been significantly 

enhanced, including generation of Scalable Vector 

Graphics (SVG) for figures [2]. The system continues

to be used as part of the infrastructure for several other 

projects such as: Planet Math24; it is used to process 

 

24 http://planetmath.org/

arXiv25 [3] manuscriptsto generate test-data for research 

in mathematical search; and in the Digital Repository of 

Mathematical Formulae (DRMF; see page 107).

Most relevant to MKM are the improvements being 

made to representation of mathematics. Extensive use of 

“parallel markup” is being used whenever the semantic 

structure of an expression is known, or inferred from 

parsing. Our parallel markup separates the presentation

form of the expression, its notations, from the content

form, what it means. This separation allows us to more 

faithfully capture the finer points of mathematical typography, preserving the intended sizes and stretchiness 

of delimiters and display style characteristics of symbols. An upcoming release of the DLMF will benefit

from these typographic improvements.

The separation also simplifies the representation of 

the semantic structure of the expression. Noting that this

structure can often be recognized during parsing even

when the exact meaning cannot; for example, it is usually clear to what expression a superscript applies, 

although it may not be certain that the superscript represents a power. We are exploring the concept of underspecified symbols to represent such cases.

The more closely the content form captures the exact meaning, the more useful it is for search indexing,

question answering and, ultimately, for computation. At 

this stage of development, the result of processing a formula is, whenever possible, a correct recognition of the 

structure, but with some subset of the symbols being ambiguous as to their meanings. The long term goal is to 

resolve such meanings through a combination of semantic analysis, type checking, and where available, 

external declarations.

Since both presentation and content branches of the 

parallel markup can be tracked to the original TeX 

25 http://arXiv.org/

Figure 81. Screen capture of a figure from TeXamples.org shown 

in a web browser. The TeX code, using the tikz package, was converted to HTML5 + SVG.
Summary of Activities for Fiscal Year 2014 107

markup, we are able to establish cross-referencing between the two branches. Such connections associate the 

meaning of a symbol with its display, or vice-versa.

In related developments, the Mathematics Markup 

Language (MathML) developed by the Math Working 

Group (BM is a member) of the World Wide Web 

Consortium (W3C) is on track to become an ISO 

standard. Also significant is the approval of HTML5 as 

a W3C recommendation; HTML5 includes MathML 

and SVG as integral components of document markup 

for the web.

[1] B. R. Miller, Three Years of DLMF: Web, Math and 

Search, Lecture Notes in Computer Science 7961 (2013), 

Springer, 288-295.

[2] B. R. Miller, D. I. Ginev and S. Oprea, E-Books and 

Graphics with LaTeXML, Lecture Notes in Artificial 

Intelligence 8543 (2014), Proceedings of the Conference 

on Intelligent Computer Mathematics, Coimbra, 

Portugal, July 7-11, 2014 (S. M. Watt, et al., eds.), 

Springer, 427-430.

[3] H. Stammerjohanns, M. Kohlhase, D. Ginev, C. David 

and B. Miller, Transforming Large Collections of 

Scientific Publications to XML, Mathematics in 

Computer Science 3:3 (2010), 299-307.

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)

Jimmy Li (Richard Montgomery High School)

Shraeya Madhu (Poolesville High School)

Azeem Mohammed (Poolesville High School)

Cherry Zou (Poolesville High School)

http://gw32.iu.xsede.org/index.php/Main_page

The goal of the NIST Digital Repository of Mathematical Formulae (DRMF) project is to build a communitybased online compendium of orthogonal polynomial and 

special function (OPSF) formulae, including related 

mathematical data, for a mathematically literate audience. The DRMF will (1) facilitate interaction among a 

community of mathematicians and scientists interested 

in compendia formulae data for orthogonal polynomials 

and special functions; (2) be expandable, allowing the 

input of new formulae from the literature; (3) represent 

the context-free full semantic information concerning 

individual formulas; (4) have a user friendly, consistent, 

and hyperlinkable viewpoint and authoring perspective; 

 

26 http://dlmf.nist.gov

(5) contain easily searchable mathematics; and (6) take 

advantage of modern MathML tools for easy to read, 

scalably rendered content-driven mathematics. Every 

formula listed in the DRMF will have its own home 

page. Our DRMF implementation is built using MediaWiki, the wiki software used by Wikipedia. See 

Figure 82 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) 26. These macros 

were invented by Bruce Miller (NIST/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 functions defined in an OPSF context. 

There are currently 546 DLMF LaTeX macros, as well 

as an additional 49 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 (1) 

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); (2) 

Koekoek, Lesky, and Swarttouw chapters 1 (Definitions 

and Miscellaneous Formulas), 9 (Hypergeometric Orthogonal Polynomials), and 14 (Basic Hypergeometric 

Orthogonal Polynomials) [4]; (3) Koornwinder KLS addendum LaTeX data [5]; (4) Bateman Manuscript 

Project (BMP) books [6]; and (5) the Wolfram Computational Knowledge of Continued Fractions Project 

(eCF).27 In August, 2014, the DRMF Project obtained 

copyright permission and license to use BMP material 

as seed content for the DRMF from Adam Cochran, Associate General Counsel of Caltech. Caltech has loaned 

us copies of the BMP. We have forwarded these copies 

to Alan Sexton, Scientific Document Analysis Group, 

School of Computer Science, University of Birmingham, UK. (Caltech is aware of this and suggested this 

was the best way to get the material to Sexton.) Sexton 

is presently scanning the BMP and developing software 

to perform mathematical optical character recognition to 

obtain LaTeX source. With regard to seed project (1), 

the DLMF source already has DLMF macros inserted. 

However for seed projects (2-5), we are developing Python software to incorporate DLMF and DRMF macros 

27 http://blog.wolframalpha.com/2013/05/16/computationalknowledge-of-continued-fractions
108 NIST Applied and Computational Mathematics Division

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, 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 server, both 

public and development instances, have 

been deployed through the XSEDE project on the Quarry cluster at Indiana 

University, Bloomington, Indiana and 

the Wikitech server of the Wikimedia 

Foundation in San Francisco.

[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, Coimbra, 

Portugal, July 7-11, 2014, (S. M. Watt, 

J. H. Davenport, A. P. Sexton, P. Sojka 

and J. Urban, eds.), Springer, 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, 2014.28

 

[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 2014.29

 

28 http://icerm.brown.edu/video_archive, see Programs and Workshops 2014 → Summer 2014 → Challenges in 21st Century

29

https://www.youtube.com/watch?v=gAGqr_4AjkI&list=UU6ulv87K

V32afXMLv6uWTW

[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.

[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. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vols. I, II, III, 

Robert E. Krieger Publishing Co., Melbourne, FL, 1981.

Figure 82. Sample DRMF Formula home page.
Summary of Activities for Fiscal Year 2014 109

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)

Michael A. Baeder (Harvey Mudd College)

Connor MacKenzie (Westminster College)

Philbert R. Hwang (Poolesville High School)

William Xu (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 natural phenomena 

such as electromagnetism, gravity, heat and waves. For 

example, in electrostatics, a Green’s function describes 

the influence of a point charge, called the source, over 

all of space. The inputs for Green’s functions are all of 

space (with the exception of a singular region), and the 

output is the “force” exerted from the point throughout 

space. Green’s functions are fundamental to the study of 

partial differential equations and are powerful in that 

they provide a mechanism for obtaining their solutions.

We 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, quaternionic, 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 

Cohl and Palmer (2014) [1] 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. We have also recently 

had success in constructing closed-form expressions of 

a fundamental solution for the Helmholtz equation is ddimensional 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 Cohl (2013) [2], a generalization of the generating function for Gegenbauer polynomials is derived 

which allows one to expand this generating function in 

terms of Gegenbauer polynomials with arbitrary order. 

This Gegenbauer polynomial expansion is useful in expanding powers of the distance between two points on 

d-dimensional Euclidean space in Vilenkin’s polyspherical coordinates. In Cohl and Volkmer (2013) [3-4], 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 Cohl, MacKenzie and Volkmer (2013) [5], generalizations of generating functions for 

hypergeometric orthogonal polynomials, namely 

Jacobi, Laguerre and Wilson polynomials are derived using connection relations with one free 

parameter and our series-rearrangement technique. 

The coefficients of these expansions are given in 

terms of generalized hypergeometric functions. 

 Cohl and MacKenzie (2013) [6] gives an extension 

of the generating function for Gegenbauer polynomials to Jacobi polynomials, and re-expresses 

Gauss hypergeometric functions in terms of more 

elementary functions for certain generating functions for classical orthogonal polynomials. 

 In Baeder, Cohl and Volkmer (2014) [7] we derive 

generalized generating functions for continuous 

hypergeometric orthogonal polynomials, namely 

Wilson, continuous Hahn, continuous dual Hahn, 

and Meixner-Pollaczek polynomials. 

 In Cohl, Costas-Santos, and Hwang (2014) [8], our 

series-rearrangement technique is extended to generalizations of generating functions for basic 

hypergeometric orthogonal polynomials. Here we 

derive generalizations of generating functions for 

Askey-Wilson, q-ultraspherical/Rogers, q-Laguerre, and little q-Laguerre/Wall polynomials. In 

collaborative research with student Xu and Baeder, we are extending this work to qhypergeometric orthogonal polynomials such as 

Al-Salam-Carlitz polynomials and for discrete hypergeometric orthogonal polynomials such as 

Meixner and Krawtchouk polynomials. As an extension of this work, in an ongoing collaborative 
110 NIST Applied and Computational Mathematics Division

research project with Palmer, we are deriving dual 

Bessel function integrals using the method of integral transforms. 

There are several connections with conferences for 

this project. For instance, Cohl is serving on both the 

Scientific Organizing and Local Organizing committees 

for the 13th International Symposium on Orthogonal 

Polynomials, Special Functions & Applications to be 

held on June 1-5, 2015 at NIST. In Berg (2015) [9], an 

open problem by Cohl is given on a very-well-poised 9F8 

generalized hypergeometric series which was presented 

at OPSFA12. Cohl is also serving on the Scientific and 

Local Organizing committees for the Orthogonal Polynomials and Special Functions Summer School 6 

workshop to be held tentatively on June 17-23, 2016 at 

American University. This OPSF Summer School is being co-organized with Daniel Lozier, Mourad Ismail, 

Stephen Casey, Erik Koelink, 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, in review.

[2] H. S. Cohl, On a Generalization of the Generating Function for Gegenbauer Polynomials, Integral Transforms 

and Special Functions 24:10 (2013), 807-816.

[3] H. S. Cohl and H. Volkmer, Separation of Variables in an 

Asymmetric Cyclidic Coordinate System, Journal of 

Mathematical Physics 54:6 (2014), 063513.

[4] H. S. Cohl and H. Volkmer, Expansions for a Fundamental Solution of Laplace’s Equation on R

3

in 5-cyclidic 

harmonics, Analysis and Applications 12:6 (2014), 613-

633. (Special Issue Dedicated to the Memory of Frank 

Olver) 

[5] H. S. Cohl, C. MacKenzie and H. Volkmer, Generalizations of Generating Functions for Hypergeometric 

Orthogonal Polynomials with Definite Integrals, Journal 

of Mathematical Analysis and Applications 407:2 (2013), 

211-225.

[6] H. S. Cohl and C. MacKenzie, Generalizations and Specializations of Generating Functions for Jacobi, 

Gegenbauer, Chebyshev and Legendre Polynomials with 

Definite Integrals, Journal of Classical Analysis 3:1

(2013), 17-33.

[7] M. A. Baeder, H. S. Cohl, and H. Volkmer, Generalizations of Generating Functions for Higher Continuous 

Hypergeometric Orthogonal Polynomials in the Askey 

Scheme, in review.

[8] H. S. Cohl, R. S. Costas-Santos, and P. R. Hwang, Generalizations of Generating Functions for Basic 

Hypergeometric Orthogonal Polynomials, in review.
Summary of Activities for Fiscal Year 2014 111

Part IV: Activity Data

 Part IV

Activity Data
112 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2014 113

Publications

Note: Names of (co-)authors with a Division affiliation 

during this reporting period are underlined.

Appeared

Refereed Journals

1. D. A. Anderson, J. B. Benson and A. J. Kearsley, 

Foundations of Modeling in Cryobiology - I: Concentration, Gibbs Energy, and Chemical Potential 

Relationships, Cryobiology 69:3 (2014), 349-360.

2. J. Bernal, C. Hagwood, J. Elliott, M. Halter and T. 

Brennan, Testing Equality of Cell Populations 

based on Shape and Geodesic Distance, IEEE 

Transactions on Medical Imaging 32:12 (2013), 

2230-2237. 

3. 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 488 (2014), 012032. 

4. J. C. Browne, R. L. DeLeon„ A. K. Patra, W. L. 

Barth, J. Hammond, M. D. Jones, T. R. Furlani, B. 

I. Schneider, S. M. Gallo, A. Ghadersohi, R. J. 

Gentner, J. T. Palmer, N. Simakov, M. Innus, A. E. 

Bruno, J. P. White, C. D. Cornelius, T. Yearke, K. 

Marcus, G. von Laszewski and F. Wang, Comprehensive Open-Source Resource Usage 

Measurement and Analysis for HPC Systems, Concurrency and Computation: Practice and 

Experience 26 (2014), 2191.

5. G. W. Bryant, N. Malkova and J. S. Sims, Mechanism for Controlling Exciton Fine Structure in 

Quantum Dots using Electric Fields: Manipulation 

of Exciton Orientation and Exchange Splitting at 

the Atomic Scale, Physical Review B 88 (2013), 

161301(R). 

6. A. S. Carasso, Compensating Operators and Stable 

Backward in Time Marching in Nonlinear Parabolic 

Equations, International Journal on Geomathematics 5 (2014), 1-16.

7. E. Cobanera, G. Ortiz and E. Knill, A Solution to 

the Non-Abelian Duality Problem, Nuclear Physics 

B 877 (2013), 574-597.

8. 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 decicated to 

the memory of Frank Olver).

9. H. S. Cohl and C. MacKenzie, Generalizations and 

Specializations of Generating Functions for Jacobi, 

Gegenbauer, Chebyshev and Legendre Polynomials 

with Definite Integrals, Journal of Classical Analysis 3:1 (2013), 17-33.

10. H. S. Cohl, C. MacKenzie and H. Volkmer, Generalizations of Generating Functions for 

Hypergeometric Orthogonal Polynomials with Definite Integrals, Journal of Mathematical Analysis 

and Applications 407:2 (2013), 211-225.

11. H. S. Cohl, On a Generalization of the Generating 

Function for Gegenbauer Polynomials, Integral 

Transforms and Special Functions 24:10 (2013), 

807-816.

12. A. Dienstfrey, F. R. Phelan Jr., S. Christensen, A. 

Strachan, F. Santosa and R. Boisvert, Uncertainty 

Quantification in Materials Modeling, JOM: The 

Journal of the Minerals, Metals and Materials Society 66:7 (2014), 1342-1344.

13. A. Dienstfrey and P. Hale, Analysis for Dynamic 

Metrology, Measurement Science and Technology

25:3 (2014), 035001.

14. A. Dienstfrey and P. Hale, Colored Noise and Regularization Parameter Selection for Waveform 

Metrology, IEEE Transactions on Instrumentation 

and Measurement 63:7 (2014), 1769-1778.

15. A. P. R. Eberle, N. Martys, L. Porcar, S. R. Kline, 

W. L. George, J. M. Kim, P. D. Butler and N. J. 

Wagner, Shear Viscosity and Structural Scalings in 

Model Adhesive Hard-Sphere Gels, Physical Review E 89 (2014), 050302. 

16. C. F. Ferraris, N. S. Martys and W. L. George, Development of Standard Reference Materials for 

Cement-Based Materials, Journal of Cement and 

Concrete Composites 54 (2014), 29-33.

17. Z. Gimbutas and S. Veerapaneni, A Fast Algorithm 

for Spherical Grid Rotations and its Application to 

Singular Quadrature, SIAM Journal on Scientific 

Computing 35:6 (2013), A2738-A2751.

18. 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.

19. 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.

20. M. Jarret and S. P. Jordan, Adiabatic Optimization 

without Local Minima, Quantum Information and 

Computation 15:3/4 (2015), 0181-0199. 
114 NIST Applied and Computational Mathematics Division

21. M. Jarret and S. P. Jordan, The Fundamental Gap 

for a Class of Schrodinger Operators on the Path 

and Hypercube Graphs, Journal of Mathematical 

Physics 55:5 (2014), 0552104.

22. S. P. Jordan, Strong Equivalence of Reversible Circuits Is CoNP-Complete, Quantum Information and 

Computation 14:15/16 (2014), 1302-1307. 

23. S. P. Jordan, K. S. M. Lee and J. Preskill, Quantum 

Computation of Scattering in Scalar Quantum Field 

Theories, Quantum Information and Computation

14:11/12 (2014), 1014-1080.

24. A. J. Kearsley, Y. Gadhyan and W. E. Wallace, Stochastic Regression Modeling of Chemical Spectra, 

Chemometrics and Intelligent Laboratory Systems

139 (2014), 26-32.

25. P. S. Kuo, J. Bravo-Abad and G. S. Solomon, Second-Harmonic Generation Using̅4-QuasiPhasematching in a GaAs Whispering-GalleryMode Microcavity, Nature Communications 5

(2014), 3109.

26. 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 58:6 (2014), 1993. 

27. H. Mahboubi, J. Habibi, A. G. Aghdam and K. Sayrafian, Distributed Deployment Strategies for 

Efficient Coverage in a Network of Mobile Sensors 

with Prioritized Sensing Field, IEEE Transactions

on Industrial Informatics 9:1 (2013), 451-461.

28. H. Mahboubi, K. Moezzi, A. G. Aghdam and K. 

Sayrafian, Distributed Deployment Algorithms for 

Efficient Coverage in a Network of Mobile Sensors 

with Non-identical Sensing Capabilities, IEEE 

Transactions on Vehicular Technology 63:8 (2014), 

3998-4016.

29. H. Mahboubi, K. Moezzi, A. G. Aghdam, K. Sayrafian and V. Marbukh, Distributed Deployment 

Algorithms for Improved Coverage in a Network of 

Wireless Mobile Sensors, IEEE Transactions on 

Industrial Informatics 10:1 (2014), 163-174. 

30. 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), 2.

31. M. Mullan and E. Knill, Simulating And Optimizing Atomic Clock Evolution, Physical Review A 90

(2014), 042310.

32. F. A. Potra, Interior Point Methods for Sufficient 

Horizontal LCP in a Wide Neighborhood of the 

Central Path with Best Known Iteration Complexity, SIAM Journal on Optimization 24:1 (2014), 1-

28.

33. I. Şahin, M. A. Simaan and A. J. Kearsley, Successive Frequency Domain Minimization for Time 

Delay Estimation, Signal Processing 98 (2014), 96-

101.

34. R. F. Sekerka, W. J. Boettinger and G. B. McFadden, Surface Morphologies due to Grooves at 

Moving Grain Boundaries Having Stress-Driven 

Fluxes, Acta Materialia 61 (2013), 7216-7226.

35. J. S. Sims and S. A. Hagstrom, Hylleraas-Configuration-Interaction Nonrelativistic Energies For The 

1 S Ground States of the Beryllium Isoelectronic 

Sequence, Journal of Chemical Physics 140 (2014), 

224312. 

36. M. J. Stevens, S. Glancy, S. W. Nam and R. P. Mirin, Third-Order Antibunching from an Imperfect 

Single-Photon Source, Optics Express 22 (2014), 

3244-3260.

37. A. Streib, N. Streib, I. Beichl and F. Sullivan, A Binomial Approximation Method for the Ising Model, 

Journal of Statistical Physics 156:3 (2014), 593-

605.

38. F. Sullivan and I. Beichl, Permanents Alpha-Permanents and Sinkhorn Balancing, Computational 

Statistics, 29:6 (2014), 1793-1798.

39. F. Vico, L. Greengard and Z. Gimbutas, Boundary 

Integral Equation Analysis on the Sphere, Numerische Mathematik 128:3 (2014), 463-487.

40. J. C. Wu, A. F. Martin and R. N. Kacker, Bootstrap 

Variability Studies In ROC Analysis On Large Datasets, Communications in Statistics - Simulation 

and Computation 43 (2014), 225-236.

41. A. C. Wilson, Y. Colombe, K. R. Brown, E. Knill, 

D. Leibfried and D. J. Wineland, Tunable Spin-Spin 

Interactions and Entanglement of Ions in Separate 

Wells, Nature 512 (2014), 57-60.

42. Y. Zhang, S. Glancy and E. Knill, Efficient Quantification of Experimental Evidence Against Local 

Realism, Physical Review A 88 (2013), 052119.

Journal of Research of NIST

1. A. S. Carasso, A Framework for Reproducible Latent Fingerprint Enhancements, Journal of 

Research of the NIST 119 (2014), 212-226.

2. B. Cloteaux, M. D. LaMar, E. Moseman and J. 

Shook, Threshold Digraphs, Journal of Research of 

the NIST 119 (2014), 227-234. 
Summary of Activities for Fiscal Year 2014 115

3. A. Pearlman, R. Datla, R. N. Kacker and C. Cao, 

Translating Radiometric Requirements for Satellite 

Sensors to Match International Standards, Journal 

of Research of NIST, 119 (2014), 272-276.

Book Chapters

1. F. Maggioni, M. Bertocchi, E. Allevi, F.A. Potra

and S. W. Wallace, Stochastic Second-Order Cone 

Programming In Mobile Ad-Hoc Networks: Sensitivity To Input Parameters, Chapter 17 in Stochastic 

Programming: Applications in Finance, Energy 

and Logistics (H. I. Gassmann, S. W. Wallace and

W. T. Ziemba, eds,), World Scientific, (2013), 467-

486.

In Conference Proceedings

1. G. Alagic, S. Jeffery and S. Jordan, Partial-Indistinguishability Obfuscation Using Braids, in 

Proceedings of the Ninth Conference on Theory of 

Quantum Computation, Communication, and Cryptography (TQC2014), (S. T. Flammia and A. W. 

Harrow, eds.), Leibnitz International Proceedings in 

Informatics 27 (2014), 141-160.

2. G. Alagic, A. Bapat and S. Jordan, Classical Simulation of Yang-Baxter Gates, in Proceedings of the 

Ninth Conference on Theory of Quantum Computation, Communication, and Cryptography

(TQC2014) ), (S. T. Flammia and A. W. Harrow, 

eds.), Liebnitz International Proceedings in Informatics 27 (2014), 161-175.

3. M. Alasti, M. Barbi and K. Sayrafian, Uncoordinated Strategies for Inter-BAN Interference 

Mitigation, in Proceedings of the IEEE 25th International Symposium on Personal, Indoor and 

Mobile Radio Communications (PIMRC 2014), 

Washington, DC, September 2014.

4. R. Alléaume, T. Chapuran, C. Chunnilall, I. Degiovanni, N. Lutkenhaus, V. Martin, M. Peev, A. 

Mink, M. Lucamarini, A. Shields and M. Ward, 

Worldwide Standardization Activity for Quantum 

Key Distribution, in Proceedings of IEEE 

Globecom 2014, Austin, TX, December 2014.

5. S. Banik, S. Sarkar and R. N. Kacker, Security 

Analysis Of The RC4+ Stream Cipher, in Progress 

in Cryptology – INDOCRYPT 2013, Lecture Notes 

in Computer Science 8250 (2013), 297-307.

6. T. Bednarz, J. A. Taylor, W. Huang, W. Griffin, S.

G. Satterfield, J. G. Hagedorn and J. Terrill, HighPerformance Visualization in Science and Research, Proceedings of IEEE Vis 2014, Paris, 

France, November 9-14, 2014, (Practitioner Experiences Poster Track).

7. H. S. Cohl, M. A. McClain, B. V. Saunders, M. 

Schubotz and J. C. Williams, Digital Repository of 

Mathematical Formulae, in Proceedings of the Conferences on Intelligent Computer Mathematics, 

Coimbra, Portugal, July 7-11, 2014, (S. M. Watt, et 

al. Eds), Lecture Notes in Artificial Intelligence

8543 (2014), 419-422.

8. 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 2-

5, 2014.

9. M. A. Davies, T. L. Schmitz and T. J. Burns, The 

Stability Of Milling: An Impact Oscillator With Delay, in Proceedings of the 17th U.S. National 

Congress on Theoretical and Applied Mechanics, 

Michigan State University, East Lansing, MI, June 

15-20, 2014. (Special Symposium in Celebration of 

Francis C. Moon's 75th Birthday)

10. C. F. Ferraris, N. S. Martys, W. L. George, Development of Standard Reference Materials for 

Cement-Based Materials, in Proceedings of the 5th 

North American Conference on the Design and Use 

of Self-Consolidating Concrete, Chicago, IL, May

12-15, 2013. 

11. J. T. Fong, N. A. Heckert, J. J. Filliben, P. V. Marcal 

and S. W. Freiman, A New Approach to Finding a 

Risk-Informed Safety Factor for “Fail-Safe” Pressure Vessel and Piping Design, in Proceedings of 

the 2014 International Symposium on Structural Integrity (ISSI), Lanzhou, China, August 20-23, 2014, 

3-23.

12. J. T. Fong, N. A. Heckert, J. J. Filliben, L. Ma, K. 

F. Stupic, K. E. Keenan and S. E. Russek, A Designof-Experiments Approach to FEM Uncertainty 

Analysis for Optimizing Magnetic Resonance Imaging RF Coil Design, in Proceedings of 2014 

International COMSOL Users Conference, Boston,

MA, October 8-10, 2014.

13. L. Ghandehari, J. Czerwonka, Y. Lei, S. Shafiee, R. 

N. Kacker and R. Kuhn, An Empirical Comparison 

of Combinatorial and Random Testing, in Proceedings of 3rd International Workshop on 

Combinatorial Testing, Cleveland, OH, March 31-

April 4, 2014, 68-77.

14. L. Ghandehari, Y. Lei, D. Kung, R. N. Kacker, R.

Kuhn, Fault Localization Based On Failure-Inducing Combinations, in Proceedings of 24th IEEE 

International Symposium on Software Reliability 

Engineering (ISSRE2013), Pasadena, CA, November 4-7, 2013, 168-177.
116 NIST Applied and Computational Mathematics Division

15. 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 

Franciso, CA, March 2014, 119-126. 

16. X. Guan, K. Bartschat, B. I. Schneider and L. 

Koesterke, Effects of Autoionizing States on TwoPhoton Double Ionization of the H2 Molecule, in 

Proceedings of the XXVIII International Conference on Photonic, Electronic and Atomic Collisions

(ICPEAC 2013) Journal of Physics: Conference Series 488 (2014), 012024.

17. J. Hagedorn, K. Sayrafian, K. Yazdandoost and J. 

Terrill, A 4D Immersive Platform to Visualize RF 

Propagation in BAN, in Proceedings of the 8th European Conference on Antennas & Propagation 

(EuCAP 2014), Den Hague, Netherlands, April 6-

11, 2014.

18. P. S. Kuo, J. S. Pelc, O. Slattery, L. Ma and X. Tang, 

Domain-Engineered PPLN for Entangled Photon 

Generation and Other Quantum Information Applications, in Nonlinear Optics and Its Applications 

VIII and Quantum Optics III (B. J. Eggleton, et al., 

eds.), Proceedings of the SPIE 9136 (2014), 

913403.

19. R. J. La, Role of Network Topology in Cybersecurity, in Proceedings of IEEE Conference on 

Decision and Control (CDC), Los Angeles, CA, 

December 2014.

20. Y.-K. Liu, Building One-Time Memories from Isolated Qubits, in Proceedings of the 5th Conference 

on Innovations in Theoretical Computer Science

(ITCS 2014), Princeton, NJ, January 12-14, 2014, 

269-286.

21. Y.-K. Liu, Single-Shot Security for One-Time 

Memories in the Isolated Qubit Model, in Advances 

in Cryptology – CRYPTO 2014, Lecture Notes in 

Computer Science 8617 (2014), 19-36.

22. H. Mahboubi, A. Aghdam, K. Sayrafian, Efficient 

Field Coverage in Mobile Sensor Networks: A CPS 

Perspective, in Proceedings of the International 

Workshop on Robotic Sensor Networks, CPS Week 

2014, Berlin, Germany, April 13-17, 2014.

23. V. Marbukh, On Systemic Risk in the Cloud Computing Model, in Proceedings of the 2014 26th 

International Teletraffic Congress (ITC), Karlskrona, Sweden, September 9-11, 2014.

24. V. Marbukh, K. Sayrafian, M. Barbi, and M. Alasti, 

Inter-BAN Interference Mitigation: A Correlated 

Equilibrium Perspective, in pHealth’14: Proceedings of 11th International Conference on Wearable 

Micro and Nano Technologies for Personalized 

Health (2014), 111-115.

25. B. R. Miller, D. I. Ginev, S. Oprea, E-Books and 

Graphics with LaTeXML E-Books and Graphics 

with LaTeXML, in Proceedings of Conference on 

ntelligent Computer Mathematics, Coimbra, Portugal, July 7--11, 2014 (S. M. Watt, et al. eds.) 

Lecture Notes in Artificial Intelligence 8543

(2014), 427-430.

26. K. Mills, C. Dabrowski, J. Filliben and S. Ressler, 

Combining Genetic Algorithms and Simulation to 

Search for Failure Scenarios in System Models, in 

Proceedings of the 5th International Conference on 

Advances in Simulation Venice, Italy (2013), 81.

27. A. Mink and A. Nakassis, LDPC Error Correction 

for Gbit/s QKD, in Defense Security & Sensing, 

Proceedings of the SPIE 9123, (2014), 912304.

28. A. Nakassis and A. Mink, Polar Codes in a QKD 

Environment, in Defense Security & Sensing, Proceedings of the SPIE 9123, (2014), 912305.

29. S. Ressler and K. Leber, Web Based 3D Visualization and Interaction for Whole Body Laser Scans, 

in Proceedings of the International Conferences on 

3D Body Scanning Technologies (2013), 166-172.

30. B. Saunders, Q. Wang and B. Antonishek, Adaptive 

Composite B-Spline Grid Generation for Interactive 3D Visualizations, in Proceedings of 

MASCOT/ISGG 2012 International IMACS/ISGG 

and Biannual Conference of Grid Generation, Las 

Palmas de Gran Canaria, Spain, October 22-26, 

2012, IMACS Series in Computational and Applied 

Mathematics 18 (2014), 241-250.

31. K. Sayrafian, J. Hagedorn, M. Barbi, J. Terrill and 

M. Alasti, A Simulation Platform to Study InterBAN Interference, in Proceedings of the 4th IEEE 

International Conference on Cognitive Infocommunications (IEEE CogInfocom 2013) (2013), 345-

350.

32. B. I. Schneider, L. A. Collins, X. Guan, K. 

Bartschat and D. Feder, Time-Dependent Computational Methods for Matter Under Extreme 

Conditions, Advances in Proceedings of the 240 

Conference: Science’s Great Challenges, (A. Dinner, ed.), Advances in Chemical Physics 157

(2014), 195-214.

33. V. Stanford, L. Diduch, A. Fillinger, K. Sayrafian, 

Connecting Medical Devices through ASTM-2761-

09: Schedule Conflict Detection Prototype, in Proceedings of the 4th Conference on Wireless Health

(2013), 20.
Summary of Activities for Fiscal Year 2014 117

34. 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, 88-92.

35. L. Yu, F. Duan, Y. Lei, R. N. Kacker, D. Richard 

Kuhn, Using Minimum Invalid Tuples to Handle 

Constraints for Combinatorial Testing of Software 

Product Lines, in Proceedings of 15th IEEE International Symposium on High Assurance Systems 

Engineering (HASE 2014) , Miami, FL, January 9-

11, 2014.

Technical Magazine Articles

1. R. Datla and R. N. Kacker, Metrological Traceability And Remote Sensing Measurements, GSICS 

Global Space-based Inter-Calibration System –

GSICS, Quarterly Newsletter 7:4 (2014).

2. Y.-K. Liu, Quantum Information: Show, Don't Tell, 

Nature Physics 10:9 (2014), 625–626.

Technical Reports

1. R. F. Boisvert (ed.), Applied and Computational 

Mathematics Division, Summary of Activities for 

Fiscal Year 2013, NISTIR 7994, March 2014.

2. H. Guan, A. Dienstfrey, M. Theofanos and B. Stanton, A Measurement Metric For Latent Fingerprint 

Processing, NISTIR 8017, July 2014.

3. F. Y. Hunt, The Structure of Optimal and Near Optimal Target Sets in Consensus Models, NIST 

Special Publication 500-303, August 6, 2014.

4. J. C. Wu, A. F. Martin, C. S. Greenberg and R. N. 

Kacker, Measurement Uncertainties of Three Score 

Distributions and Two Thresholds with Data Dependency, NISTIR 8025, September, 2014.

Accepted

1. A. Anandkumar, D. P. Foster, D. Hsu, S. M. Kakade 

and Y.-K. Liu, A Spectral Algorithm for Latent Dirichlet Allocation, Algorithmica.

2. 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 the Mechanics and Physics of Solids.

3. J. Chen, J. Terill, H. Zhao, G. Zhang, K. Wu, A. 

Garbrino and Y. Zhu, Interactive Visual Computing 

Laboratory Research, IEEE Virtual Reality, Arles, 

Camargue, Provence, France, March 23-27, 2015. 

4. 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 Environments, 

VR2015 IEEE Virtual Reality, Arles, Camargue, 

Provence, France, March 23-27, 2015. 

5. R. Datla and R. N. Kacker, Calibration Considerations for Mission Success, NIST Handbook: 

Guidelines for Radiometric Calibration of ElectroOptical Instruments for Remote Sensing.

6. G. Doğan, An Efficient Curve Evolution Algorithm 

for Multiphase Image Segmentation, International 

Conference on Energy Minimization Methods in 

Computer Vision and Pattern Recognition 

(EMMCVPR), Hong Kong, January 13-16, 2015.

7. W. Griffin, D. Catacora, S. Satterfield, J. Bullard, J. 

Terrill, Incorporating D3.js Information Visualization into Immersive Virtual Environments (poster), 

IEEE Virtual Reality, Arles, France, March 23-27, 

2015.

8. J. D. Hagar, R. Kuhn, R. N. Kacker, T. L. Wissink, 

Introducing Combinatorial Testing to a Large System-Software Organization, IEEE Computer.

9. E. Knill, S. Glancy, S. W. Nam, K. Coakley and Y. 

Zhang, Bell Inequalities for Continuously Emitting 

Sources, Physical Review A.

10. 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.

11. R. J. La, Interdependent Security with Strategic 

Agents and Global Cascades, IEEE/ACM Transactions on Networking.

12. J. F. Lawrence, R. N. Kacker and R. Kessel, 

Obtaining a Trapezoidal Distribution, 

Communications in Statistics – Theory and 

Methods.

13. H. Mahboubi, A. Aghdam, and K. Sayrafian, Selfdeployment Algorithms for Coverage Improvement 

in Mobile Sensor Networks in Presence of Obstacles, in Control and Systems Engineering - A Report 

on Decades of Contribution.

14. R. F. Sekerka, S. R. Coriell and G. B. McFadden, 

Morphological Stability, in Handbook of Crystal 

Growth.

15. 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.
118 NIST Applied and Computational Mathematics Division

In Review

1. D. A. Anderson, J. B. 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.

2. M. A. Baeder, H. S. Cohl and H. Volkmer, Generalizations of Generating Functions for Higher 

Continuous Hypergeometric Orthogonal Polynomials in the Askey Scheme.

3. I. Beichl and Y. Kemper, Monte Carlo Methods to 

Approximate the Chromatic Polynomial.

4. J. Bernal, NEURBT: A Program for Computing 

Neural Networks for Classification using Batch 

Learning.

5. A. S. Carasso, Stable Explicit Time Marching In 

Well-Posed and Ill-Posed Nonlinear Parabolic 

Equations.

6. A. S. Carasso and A. E. Vladar, Recovery of Background Structures in Nanoscale Helium Ion 

Microscope Imagery.

7. H. S. Cohl and R. M. Palmer, Fourier and Gegenbauer Expansions for a Fundamental Solution of 

Laplace's Equation in Hyperspherical Geometry.

8. H. S. Cohl, R. S. Costas-Santos and P. R. Hwang, 

Generalizations of Generating Functions for Basic 

Hypergeometric Orthogonal Polynomials.

9. J. Diemunsch, M. Ferrara, S. Jahanbekam and J. 

Shook, Extremal Theorem for Packing a Degree Sequence with a Graph.

10. G. Doğan, J. Bernal and C. Hagwood, A Fast Algorithm for Elastic Shape Distances between Closed 

Planar Curves.

11. G. Doğan, J. Bernal and C. Hagwood, Fast Algorithm for Alignment of 2D Closed Curves with 

Application to Elastic Shape Analysis.

12. 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.

13. 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.

14. Z. Gimbutas and L. Greengard, A Fast Multipole 

Method for the Evaluation of Elastostatic Fields in 

a Half-Space with Zero Normal Stress.

15. W. Griffin and M. Olano, Evaluating Texture Compression Masking Effects using Objective Image 

Quality Assessment Metrics.

16. A. Gueye, P. Mell, R. Harang and R. J. La, Moving 

Target Defenses with Security Checkpoints in IPv6 

Networks.

17. A. Gueye and A. Lazska, Network Topology Vulnerability/Cost Tradeoff: Model, Application, and 

Computational Complexity. 

18. A. Harvey, E. Simiu, F. A. Potra, K. Quinlan and N. 

Chokshi, Design-Basis Hurricane Winds and Missiles for Nuclear Power Plants.

19. S. P. Jordan, K. S. M. Lee and J. Preskill. Quantum 

Algorithms for Fermionic Quantum Field Theories.

20. R. N. Kacker, Probability Distributions and Coverage Probability in GUM, JCGM Documents, and 

Statistical Inference.

21. Y. Kemper and I. Beichl, Importance Sampling to 

Approximate the Coefficients of the Chromatic Polynomial.

22. R. J. La, Effects Of Degree Distributions On Network Security — Population Game Model. 

23. 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.

24. Y.-K. Liu, Privacy Amplification in the Isolated 

Qubits Model.

25. 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.

26. F. Maggioni, F. A. Potra and M. Bertocchi, Stochastic Versus Robust Optimization for a Supply 

Transportation Problem.

27. H. Mahboubi, A. Aghdam and K. Sayrafian,

Maximum Lifetime Strategy for Target Monitoring 

with Controlled Node Mobility in Sensor Networks 

with Obstacles.

28. H. Mahboubi, A. Aghdam and K. Sayrafian, A Joint 

Relocation and Sensing Range Algorithm to Improve Coverage and Lifetime in Wireless Mobile 

Sensor Networks.

29. H. Mahboubi, A. Aghdam and K. Sayrafian, An 

Energy-Efficient Target Tracking Strategy for 

Mobile Sensor Networks.

30. P. Mell, R. Harang, A. Gueye, The Resilience of the 

Internet to Colluding Country Induced Connectivity 

Disruptions.
Summary of Activities for Fiscal Year 2014 119

31. J. L. Molaro, S. Byrne and S. A. Langer, GrainScale Thermoelastic Stresses and Spatiotemporal 

Temperature Gradients on Airless Bodies, Implications for Rock Breakdown.

32. A. Nucciotti, B. Alpert, M. Balata, D. Bennett, M. 

Biasotti, C. Boragno, C. Brofferio, V. Ceriale, M. 

De Gerone, M. Faverzani, E. Ferri, J. Fowler, F. 

Gatti, A. Giachero, M. Lusignoli, G. Hilton, U. 

Koester, M. Maino, J. Mates, S. Nisi, R. Nizzolo, 

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, The HOLMES Experiment. 

33. 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.

34. J. Penczek, S. G. Satterfield, E. F. Kelley, D. G. 

Hulme, T. Scheitlin, J. Terrill and P. A. Boynton, 

Evaluating the Visual Performance of Stereoscopic 

Immersive Display Systems.

35. F. A. Potra, Sufficient Weighted Complementarity

Problems.

36. S. Pourarian, J. Wen, A. J. Kearsley and A. Pertzborn, Efficient and Robust Optimization for 

Building Energy Simulation.

37. R. Pozo, Q-Matrix: An Algebraic Formulation for 

the Analysis and Visual Characterization of Network Graphs.

38. 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.

39. J. Shook and I. Beichl, Matrix Scaling: A New Heuristic for the Feedback Vertex Set Problem.

40. J. Sifuentes, Z. Gimbutas and L. Greengard, Randomized Methods for Rank-Deficient Linear 

Systems.

41. J. Stoian, T. Oey, J. Huang, A. Kumar, J. W. 

Bullard, M. Balonis, S. G. Satterfield, J. Terrill, N. 

Neithalath and G. Sant, Prehydration of Ordinary

Portland Cement and its Mitigation using Limestone: New Insights from Experiments and 

Simulations.

42. A. Streib, N. Streib, I. Beichl and F. Sullivan, Stratified Sampling for the Ising Model — A Graph 

Theoretic Approach.

43. F. Vico, L. Greengard, M. Ferrando and Z. Gimbutas, The Decoupled Potential Integral Equation for 

Time-Harmonic Electromagnetic Scattering.

Invention Disclosures

1. A. S. Carasso and A. E. Vladar, Recovery Of Background Structures in Nanoscale Helium Ion 

Microscope Imagery, and the Use of Progressive 

Levy Fractional Diffusion Smoothing, NIST Office 

of Technology Partnerships, May 2013.

Presentations

Invited Talks

1. B. Alpert, “Efficiency-Enhanced Hybrid GaussTrapezoidal Quadrature Rules,” Integral Equations 

Methods: Fast Algorithms and Applications, Banff 

International Research Station, December 9, 2013.

2. B. Alpert, “Mathematical Challenges in HighThroughput Microcalorimeter Spectroscopy,” IMA 

Workshop on Math Modeling in Industry, Vancouver, B.C., August 6, 2014.

3. R. F. Boisvert, “Measurement Science for Information Systems,” Bell Labs – NIST Workshop on 

Large Scale Networks, Alcatel-Lucent Bell Laboratories, Murray Hill, NJ, October, 25, 2013.

4. R. F. Boisvert, “Network Science at NIST,” Joint 

University of Maryland – NIST Workshop in Network Science, College Park, MD, January 24, 2014.

5. R. F. Boisvert, “Computer Science Research in a 

Federal Lab,” Department of Computer Science, 

George Washington University, March 28, 2014.

6. B. Cloteaux, “Information and Heuristics Creation,” Mathematics Colloquium, George Mason 

University, Fairfax, VA, November 8, 2013.

7. B. Cloteaux, “Information and Heuristics Creation,” Statistics Colloquium, George Mason

University, Fairfax, VA, November 15, 2013.

8. H. S. Cohl, “Generalizations of Generating Functions for Orthogonal Polynomials in the Askey and 

q-Askey Schemes Analysis,” Departamento de Matematica, Universidade de Coimbra, Portugal, July 

9, 2014.

9. H. S. Cohl, M. Baeder, P. R. Hwang and H. 

Volkmer, “Generalizations of Orthogonal Polynomials in Askey Schemes,” Department of 

Mathematics and Statistics Colloquium, American 

University, Washington, DC, April 15 2014.

10. H. S. Cohl, “Outgrowths of the Digital Library of 

Mathematical Functions Project: NIST Digital Repository of Mathematical Formulae,” Challenges in 

21st Century Experimental Mathematical Computation Conference, Institute for Computational and 
120 NIST Applied and Computational Mathematics Division

Experimental Research in Mathematics, Brown 

University, Providence, RI, July 21, 2014.

11. H. S. Cohl, “XSEDE and the NIST Digital Repository of Mathematical Formulae,” XSEDE Science 

Gateways Community Series, August 29, 2014.

12. S. Colbert-Kelly, “A Generalized Ginzburg-Landau 

model in a Planar Geometry,” Department of Mathematical Sciences Colloquium, New Mexico State 

University, Las Cruces, NM, November 14, 2013.

13. S. Colbert-Kelly, “A Generalized Ginzburg-Landau 

model in a Planar Geometry,” Howard University 

Mathematics Colloquium, Howard University, 

Washington, D.C., March 21, 2014.

14. S. Colbert-Kelly, “A Generalized Ginzburg-Landau 

model in a Planar Geometry,” Applied and Computational Mathematics Seminar, George Mason 

University, Fairfax, VA, May 2, 2014.

15. G. Doğan, “Shape Optimization for Image Analysis," Applied and Computational Mathematics 

Seminar, George Mason University, Fairfax, VA, 

April 11, 2014.

16. J. T. Fong, “A Risk-informed and ContinuousMonitoring Approach to Fail-Safe Operation of Aging Pressure Vessels and Piping,” China National 

Conference on Pressure Vessel Technology, Hefei, 

China, November 9, 2013.

17. J. T. Fong, “A Fail-Safe Design and Operation 

Methodology Based on Lessons Learned from the 

2011 Fukushima Reactor Meltdown Incident,” University of California-Irvine and National Academy 

of Engineering Joint Meeting on the Materials Genome, Beckman Center, Irvine, CA, February 11, 

2014.

18. J. T. Fong, “Uncertainty Analysis of A Class of 

FEM-based Solutions Using the COMSOL Radio 

Frequency (RF), and MEMS Modules,” Electromagnetics Division, NIST, Boulder, CO, April 3, 

2014.

19. J. T. Fong, “Uncertainty Estimation and Model Validation for NDE-Based Electromagnetics Solutions 

Using ABAQUS and COMSOL,” Department of 

Civil and Environmental Engineering, University of 

South Carolina, Columbia, SC, May 1, 2014.

20. J. T. Fong, “A New Approach to Risk-based Definition of Engineering Safety Factors Using (1) the 

Bootstrap Method to Estimate the Weibull Location 

Parameter, and (2) The Lower Tolerance Limit to 

Estimate a Safety Factor,” Department of Statistics, 

University of South Carolina, Columbia, SC, May 

2, 2014.

21. J. T. Fong, “Multi-Scale Modeling, Uncertainty Estimation, and Model Validation for Predicting 

Remaining Life of Aging Structures and Components,” VTD/Mechanics Division, U.S. Army 

Research Laboratory, Aberdeen Proving Ground, 

MD, May 7, 2014.

22. J. T. Fong, “A Fail-Safe Approach to Risk-Informed Modeling of Fatigue of Aging Structures 

and Components,” ICCES Lifetime Achievement 

Medal Award Lecture, International Conference on 

Computational and Experimental Sciences and Engineering, Changwon, South Korea, June 14, 2014.

23. J. T. Fong, “Automated Massive NDE Image Analysis, and Feature Abstracting for Fatigue Modeling 

of Aging Structures,” 41st Quantitative Nondestructive Evaluation (QNDE) Meeting, Boise, ID, July 

22, 2014.

24. J. T. Fong, “Model Selection and Experimental Design for NDE Engineers,” Department of 

Mechanical and Power Engineering, Lanzhou University of Technology, Lanzhou, China, August 18, 

2014.

25. J. T. Fong, “A New Approach to Finding a RiskInformed Safety Factor for Fail-Safe Pressure Vessel and Piping Design,” International Symposium 

on Structural Integrity, Lanzhou, China, August 21, 

2014.

26. J. T. Fong, “Multi-Scale Modeling, Uncertainty Estimation, and Model Validation for Designing New 

Materials and Predicting Fatigue Life of Aging 

Structures,” NASA Glenn Research Center, Cleveland, OH, September 10, 2014.

27. J. T. Fong, “Uncertainty Quantification in Fatigue 

and Risk Modeling,” U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, September

12, 2014. 

28. S. Glancy, “Bell Inequalities for Time-tagged Detections,” Quantum Theory: from Problems to 

Advances, Linnéuniversitetet, Växjö, Sweden, June 

9, 2014.

29. A. Gueye, “Science-Based Metrics for Network Topology Resilience against Attacks,” Mathematical 

Sciences Colloquium, College of Sciences, George 

Mason University, Fairfax, VA, October 18, 2013.

30. F. Hunt, “Optimal and Near Optimal Sets for the 

Spread of Consensus in a Network Model,” Joint 

University of Maryland – NIST Workshop in Network Science, College Park, MD, January 24, 2014.

31. A. J. Kearsley, “Optimization and Chemical Spectroscopy at NIST,” SIAM Student Chapter Meeting, 

University of Delaware, February 28, 2014.
Summary of Activities for Fiscal Year 2014 121

32. E. Knill, “Certifying Violations of Local Realism,” 

Southwestern Quantum Information Technology 

Workshop (SQUINT), February 22, 2014.

33. E. Knill, “Certifying Violations of Local Realism,” 

Workshop on Quantum Information and Computer 

Science, College Park, MD, April 1, 2014.

34. P. S. Kuo, “Second-Harmonic Generation in GaAs 

Whispering-Gallery-Mode Microcavities,” QIBEC 

Seminar, NIST, Gaithersburg, MD, February 18, 

2014.

35. R. J. La, “Cascades in Interdependent Security with 

Strategic Players,” Information Theory and Applications (ITA) Workshop, San Diego CA, February

2014.

36. Y.-K. Liu, “Tamper-Resistant Cryptographic Hardware in the Isolated Qubits Model,” 4th 

International Conference on Quantum Cryptography (QCrypt 2014), Paris, France, September 1-

5, 2014.

37. G. B. McFadden, “Bubble Motion and Size Variation during Thermal Migration with Phase 

Change,” Materials Science and Technology 2013, 

Montreal, Canada, October 28, 2013.

38. D. G. Porter, “State of Tcl”, 21st Annual Tcl/Tk 

Conference, Portland, OR, November 13, 2014.

39. F. A. Potra, “Weighted Complementarity Problems,” AMS Spring Eastern Sectional Meeting, 

UMBC, Baltimore, MD, March 29-30, 2014.

40. R. Pozo, “A Network Measure for the Analysis of 

Large-Scale Graphs,” Joint University of Maryland 

– NIST Workshop in Network Science, College 

Park, MD, January 24, 2014.

41. R. Pozo, “A Network Measure For The Analysis Of 

Large-Scale Graphs,” Applied Dynamics Seminar, 

University of Maryland, College Park, MD, March 

27, 2014.

42. S. Ressler, “Declarative 3D Graphics for the Web, 

Integrating X3DOM, jQuery, WebGL and 

HTML5,” Gettysburg College, Gettysburg, PA, October 10, 2013.

43. S. Ressler, “What's That 3D Model Doing in my 

Web Browser?” NIST Model-Based Enterprise 

Summit 2014, Gaithersburg, MD, December 17, 

2014.

44. K. Sayrafian, “A 4D Immersive Platform to Visualize RF Propagation in BAN”, the 8th European 

Conference on Antennas & Propagation (EuCAP 

2014), Den Hague, Netherlands, April 6-11, 2014. 

45. K. Sayrafian, “A Simulation Platform to Study Inter-BAN Interference”, IEEE International 

Conference on Cognitive Infocommunications, Budapest, Hungary, December 2-5, 2013.

46. J. Shook, “Threshold Digraphs,” Combinatorics 

Seminar, George Mason University, VA, April 18, 

2014.

47. J. Shook, “Matrix Scaling: A New Heuristic for the 

Feedback Vertex Set Problem,” Mathematical Sciences Colloquium, George Mason University, VA, 

April 18, 2014.

48. J. Shook, “Matrix Scaling: A New Heuristic for the 

Feedback Vertex Set Problem,” Discrete Mathematics Seminar, University of Colorado at Denver, 

CO, April 28, 2014

49. J. Terrill, “Science,” Keynote Lecture, 25th Annual 

Females in Science and Technology Conference, 

Montgomery Blair High School, Silver Spring, 

MD, March 22, 2014. 

50. J. Terrill, “Parallel Universes, Perpendicular 

Thinking, and Scientific Results,” Keynote Lecture,

Effective Visualization for Science and eResearch, 

Melbourne, Australia, March 29, 2014.

Conference Presentations

1. B. Antonishek, “Look Ma—no Plug-in! (DLMF’s 

New WebGL 3D Figures),” Web3D 2014, 19th International Conference on 3D Web Technology, 

Vancouver, Canada, August 10, 2014.

2. T. Bednarz, J. A. Taylor, W. Huang, W. Griffin, L. 

S. G. Satterfield, J. G. Hagedorn, J. Terrill, “HighPerformance Visualization in Science and Research,” Practitioner Experiences Poster Track, 

IEEE Vis 2014, Paris France, November 9-14, 

2014. 

3. H. S. Cohl, “Digital Repository of Mathematical 

Formulae,” Conferences on Intelligent Computer 

Mathematics, Coimbra, Portugal, July 10, 2014.

4. H. S. Cohl, M. Baeder and H. Volkmer, “Generalizations of Generating Functions for 

Hypergeometric and Q-Hypergeometric Orthogonal Polynomials,” Spring American Mathematical 

Society Central Sectional Meeting, Texas Tech 

University, Lubbock, Texas, April 11, 2014.

5. S. Colbert-Kelly, “Analysis of Point Defects in a 

Ferroelectric Liquid Crystal Using a Generalized 

Ginzburg-Landau Model,” 2013 SIAM Conference 

on Analysis of Partial Differential Equations, Lake 

Buena Vista, FL, December 8, 2013.

6. G. Doğan, “Segmentation of Microstructure Images,” Material Knowledge Systems Workshop, 

NIST, Gaithersburg, MD, January 13, 2014.
122 NIST Applied and Computational Mathematics Division

7. G. Doğan, “A Fast Algorithm to Compute the Shape 

Dissimilarity of Elastic Curves,” 13th Copper 

Mountain Conference on Iterative Methods, Copper 

Mountain, CO, April 9, 2014.

8. G. Doğan, “An Adaptive Shape Reconstruction Algorithm for Inverse Problems,” SIAM Conference 

on Imaging Science, Hong Kong, May 12, 2014.

9. G. Doğan, “Minimization of Curvature Energies 

with Applications in Image Processing,” International Conference on Advances in Applied 

Mathematics and Mathematical Physics 

(ICAAMMP), Istanbul, Turkey, August 19, 2014.

10. G. Doğan, “A Python Toolbox for Shape Optimization in Image Processing,” European Conference on 

Python in Science (EuroScipy), Cambridge, UK, 

August 28, 2014.

11. M. Donahue, “A Fourth Order Demagnetization 

Tensor for Rectangular Prisms,” 58th Annual Magnetism and Magnetic Materials Conference, 

Denver, CO, November 6, 2013.

12. M. Donahue, “Implementation of a Localized 

Fourth Order Demagnetization Tensor,” 59th Annual Magnetism and Magnetic Materials 

Conference, Honolulu, HI, November 5, 2014.

13. Z. Gimbutas and A. Dienstfrey, “MRI simulators 

and their Performance,” NIST Workshop on Standards for Quantitative MRI, NIST, Boulder, CO, July 

16, 2014.

14. Z. Gimbutas, “Interpolation and Integration in 

Spaces of Singular Functions,” Workshop 

13w5044, Integral Equations Methods: Fast Algorithms and Applications, Banff International 

Research Station for Mathematical Innovation and 

Discovery (BIRS), Banff, Canada, December 9, 

2013.

15. S. Glancy, “Practical and Fast Gaussian State Estimation,” Southwest Quantum Information 

Technology (SQUINT) Workshop, Sante Fe, NM, 

February 22, 2014.

16. W. Griffin and M. Olano, “Objective Image Quality 

Assessment of Texture Compression,” ACM 

SIGGRAPH Symposium on Interactive 3D 

Graphics and Games (I3D), San Franciso, CA, 

March 15, 2014. 

17. X. Guan, K. Bartschat, B. I. Schneider and L. 

Koesterke, “Two-Photon Double-Ionization of the 

H2 Molecule in Light Perpendicular to the Internuclear Axis: Effects of Pulse Duration,” 45th Annual 

Meeting of the APS Division of Atomic, Molecular 

and Optical Physics, Madison, WI, June 2–6, 2014.

18. A. Gueye, A. Lazska, “Network Topology Robustness under Adversarial Environment and Budget 

Constraints: General Model and Computational 

Complexity”, GameSec 2013, Fort Worth, TX, November 11-12, 2013.

19. R. N. Kacker “Coverage Probability in GUM, 

GUM-S1, VIM, and Statistical Inference,” International Workshop on Mathematics and Statistics for 

Metrology (MATHMET-2014), Berlin, Germany, 

March 24-26, 2014.

20. P. S. Kuo, “Spectral Response and Characterization 

of a High-Efficiency Upconvertor for Single-Photon-Level Detection,” Single Photon Workshop, 

Oak Ridge, TN, October 18, 2013.

21. P. S. Kuo, “Polarization-Entangled Photons from 

Domain-Engineered, Periodically Poled LiNbO3,”

CLEO Conference, San Jose, CA, June 9, 2014.

22. R. J. La, “Role of Network Topology in Cybersecurity,” IEEE Conference on Decision and Control 

(CDC), Los Angeles, CA, December 17, 2014.

23. Y.-K. Liu, “Building One-Time Memories from 

Isolated Qubits,” 5th Conference on Innovations in 

Theoretical Computer Science (ITCS 2014), 

Princeton, NJ, January 12-14, 2014.

24. Y.-K. Liu, “Single-Shot Security for One-Time 

Memories in the Isolated Qubits Model,” 17th Conference on Quantum Information Processing (QIP 

2014), Barcelona, Spain, February 3-7, 2014.

25. Y.-K. Liu, “Single-Shot Security for One-Time 

Memories in the Isolated Qubits Model,” 34rd International Cryptology Conference (CRYPTO 

2014), Santa Barbara, CA, August 17-21, 2014.

26. D. W. Lozier, “Outgrowths of the Digital Library of 

Mathematical Functions Project Part 1: DLMF 

Standard Reference Tables,” ICERM Workshop on 

Challenges in 21st Century Experimental Mathematical Computation, Providence, RI, July 21, 

2014.

27. V. Marbukh, “On Systemic Risk in the Cloud Computing Model,” 26th International Teletraffic 

Congress (ITC 26), Karlskrona, Sweden, September 9-11, 2014.

28. V. Marbukh, K. Sayrafian, M. Barbi and M. Alasti, 

“Inter-BAN Interference Mitigation: A Correlated 

Equilibrium Perspective,” 11th International Conference on Wearable Micro and Nano Technologies 

for Personalized Health (pHealth’14), Vienna, Austria, June 11-13, 2014. 

29. N. S. Martys, D. Lootens, W. L. George, P. Hebraud 

and M. Liard, “Universal Scaling Of Microscopic 
Summary of Activities for Fiscal Year 2014 123

And Macroscopic Behavior In Spherical Non-Colloidal Suspensions With A Non-Newtonian Fluid 

Matrix,” Society of Rheology 85th Annual Meeting, Montreal, Quebec, Canada, October 13-17, 

2013. 

30. G. B. McFadden, “A Cross-Benchmarking and Validation Initiative for Tokamak 3D Equilibrium 

Calculations,” 56th Annual Meeting of the APS Division of Plasma Physics, New Orleans, LA, 

October 28, 2014.

31. B. R. Miller, D. I. Ginev, S. Oprea, E-Books and 

Graphics with LaTeXML, Conference on Intelligent Computer Mathematics, Coimbra, Portugal, 

July 10, 2014.

32. W. F. Mitchell, “Recent Advances in PHAML,” 

SIAM Conference on Parallel Processing for Scientific Computing, Portland, OR, February 18, 2014.

33. W. F. Mitchell and M. A. McClain, “Performance 

of hp-Adaptive Strategies for Elliptic Partial Differential Equations,” 12th International Conference of 

Numerical Analysis and Applied Mathematics, 

Rhodes, Greece, September 24, 2014.

34. W. F. Mitchell and M. A. McClain, “Performance 

of hp-Adaptive Strategies for Elliptic Partial Differential Equations,” International Conference on 

Spectral and High Order Methods, Salt Lake City, 

UT, June 24, 2014.

35. R. Pozo, “Extending Q-Matrix Frameworks for 

Generalized Network Centralities,” SIAM Workshop on Network Science, Chicago, IL, July 7, 

2014.

36. S. Ressler, “Web Based 3D Visualization and Interaction for Whole Body Laser Scans,” Hometrica 

2013 3D Body Scanning Technologies Conference, 

Long Beach, CA, Nov 2013.

37. 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. 

38. S. Ressler, “Web 3D Showcase,” Web3D 2014, 

Vancouver, Canada, August 11, 2014.

39. B. Rust and K. Mullen, “The Metrology of Supernova Lightcurves,” 223rd Meeting of the American 

Astronomical Society, Washington, DC, January 6, 

2014.

40. B. Rust and M. Leventhal, “Evidence for Accelerated Radioactive Decay (ARD) Models of 

Supernova Lightcurves in the Low Redshift Universe,” 224th Meeting of the American 

Astronomical Society, Boston, MA, June 2, 2014.

41. B. Rust, “The Metrology of Type Ia Supernova 

Lightcurves,” 225th Meeting of the American Astronomical Society, Seattle, WA, January 5, 2015.

42. B. Saunders, “Using Adaptive Composite B-Spline 

Grid Generation to Enhance 3D Web Visualizations,” SIAM Conference on Geometric and 

Physical Modeling (GD/SPM13), Denver, CO, November 14, 2013.

43. B. Saunders, “WebGL: Interactive 3D Graphics on 

the Web without a Plugin,” MAA MD-DC-VA 

Spring Section Meeting, James Madison University, Harrisonburg, VA, April 26, 2014.

44. B. Saunders, Q. Wang, B. Antonishek, B. Miller, 

“Adaptive Composite B-Spline Mesh Generation 

for 3D Visualization,” 8th International Conference 

on Curves and Surfaces, Paris, France, June 17, 

2014.

45. K. Sayrafian, “Efficient Field Coverage in Mobile 

Sensor Networks: A CPS Perspective,” International Workshop on Robotic Sensor Networks, CPS 

Week, Berlin. Germany, April 14, 2014.

46. K. Sayrafian, “Energy Harvesting from Human Leg 

Motion,” 8th International Conference on Pervasive

Computing Technologies for Healthcare (Pervasive 

Health 2014), Oldenberg, Germany, May 21, 2014.

47. K. Sayrafian, “Uncoordinated Strategies for InterBAN Interference Mitigation,” IEEE 25th Annual 

International Symposium on Personal, Indoor and 

Mobile Radio Communications (PIMRC 2014),

Washington, DC, September 2, 2014.

48. K. Sayrafian, “Maximizing Output Power of a 

CFPG Micro Energy-Harvester for Wearable Medical Sensors,” 4th International Conference on 

Wireless Mobile Communication and Healthcare 

(MobiHealth 2014), Athens, Greece, November 5, 

2014.

49. 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.

50. J. Terrill, “Immersive Visualization at NIST, Birds 

of a Feather (BOF),” Immersive Visualization for 

Science and Research, 41st International Conference and Exhibition on Computer Graphics and 

Interactive Technologies, SIGGRAPH 2014, August 11, 2014, Vancouver, CA.
124 NIST Applied and Computational Mathematics Division

Poster Presentations

1. T. Bednarz, J. A. Taylor, W. Huang, W. Griffin, S.

G. Satterfield, J. G. Hagedorn and J. Terrill, “HighPerformance Visualization in Science and Research,” Practitioner Experiences Poster Track,

IEEE Vis 2014, Paris, France, November 9-14, 

2014.

2. A. J. Kearsley, “Stochastic Regression Modeling of 

Noisy Spectra,” PITTCON Conference and Expo, 

Chicago IL, March 4, 2014. 

3. A. J. Kearsley, “Analysis of Chemical Spectra by 

Stochastic Regression, Stochastic Processes and 

Applications,” Buenos Aires, Argentina, July 30, 

2014. 

4. P. S. Kuo, “Quantum Communications Research at 

NIST Information Technology Laboratory,” Workshop on Quantum Information and Computer 

Science, College Park, MD, March 31, 2014.

5. A. Gueye and R. J. La, “Influence of Assortativity 

on Network Security,” International Conference on 

Network Science (NetSci), Berkeley, CA, June 5, 

2014. 

6. V. Marbukh, “Systemic Risk/Benefits of Interconnectivity due to Metastability,” International 

Conference on Network Science (NetSci), Berkeley, CA, June 5, 2014.

7. V. Marbukh, “Eigenvector Centrality Localization 

and Hierarchy of Important Spreaders in LargeScale Networks,” NetSci, Berkeley, CA, June 5, 

2014.

8. P. Mell, R. Harang and A. Gueye, “The Resilience 

of the Internet to Colluding Country Induced Connectivity Disruptions,” MPACT Week, University 

of Maryland, College Park, MD, October 17, 2014.

Web Services

1. Adaptive Mesh Refinement Benchmark Problems30: a collection of partial differential equations 

suitable for testing and benchmarking adaptive 

mesh refinement algorithms.

2. AnthroWeb3DMeasure31: A tool for Web3D based 

anthropometric visualization and measurement.

 

30 http://math.nist.gov/amr-benchmark

31 http://math.nist.gov/~SRessler/x3dom/aw3dm.xhtml

32 http://dlmf.nist.gov/

33 http://dlmftables.uantwerpen.be/

34 http://gams.nist.gov/

35 http://math.nist.gov/matrixmarket/

36 http://www.ctcms.nist.gov/mumag/mumag.org.html

3. Digital Library of Mathematical Functions32: a repository of information on the special functions of 

applied mathematics.

4. DLMF Standard Reference Tables on Demand33: 

tables of values for special functions, with guaranteed accuracy to high precision. 

5. Guide to Available Mathematical Functions34: a virtual repository of mathematical software 

components. (dormant)

6. Matrix Market35: a repository of matrices for testing 

of algorithms and software for numerical linear algebra. (dormant)

7. μMAG36: a collection of micromagnetic reference 

problems and submitted solutions.

8. SciMark37: a benchmark for scientific computing in 

Java. (dormant)

Software Released

1. ACTS38: Combinatorial test suite generation with 

support of constraints. Version 2.9 – Y. Lei, R. N. 

Kacker, D. R. Kuhn.

2. LaTeXML39: A LaTeX to XML converter. Version 

0.8.0 – B. R. Miller.

3. OOF240: Finite element modeling of material microstructures. Version 2.1.11 – S. Langer.

4. OOF3D41: Finite element modeling of material microstructures in 3D. Version 3.0.0 – S. Langer and 

Yannick Congo.

5. OOMMF42: Object Oriented MicroMagnetic 

Framework. Version 1.2a5bis — D. Porter and M. 

Donahue.

6. PHAML43: Solution of elliptic partial differential 

equations using finite elements, hp-adaptive refinement and multigrid methods. Version 1.14.0 – W. 

F. Mitchell.

7. Itcl: C++ inspired object oriented commands for 

Tcl. Versions 4.0.1, 4.0.2 – D. G. Porter.

8. sqlite3: Bindings to the SQLite database engine for 

Tcl. Versions 3.8.4.3, 3.8.5, 3.8.6, 3.8.7.1 – D. G. 

Porter.

37 http://math.nist.gov/scimark/

38 http://csrc.nist.gov/groups/SNS/acts/

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

40 http://www.ctcms.nist.gov/oof/oof2/index.html

41 http://www.ctcms.nist.gov/oof/oof3d/

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

43 http://math.nist.gov/phaml/
Summary of Activities for Fiscal Year 2014 125

9. Tcl/Tk44: Extensible scripting language and GUI 

toolkit. Versions 8.5.16, 8.5.17, 8.6.2, 8.6.3 – D. G. 

Porter.

10. TDBC: Database connection commands for Tcl. 

Versions 1.0.1, 1.0.2 - D. G. Porter.

11. Thread: Thread management commands for Tcl. 

Version 2.7.1 - D. G. Porter.

Conferences, Minisymposia, 

Lecture Series, Courses

ACMD Seminar Series

B. Cloteaux served as Chair of the ACMD Seminar Series. There were 22 talks presented during this period; 

all talks are listed chronologically. 

1. M. Enriquez (MITRE), “Systemizing the Solution of 

Simulation-Driven Optimization Problems,”

November 26, 2013.

2. H. Antil (George Mason University), “Optimal 

Control of Free Boundary Problems with Surface 

Tension Effects,” December 3, 2013.

3. S. Kimmel (MIT), “Quantum Adversary Upper 

Bound,” December 17, 2013.

4. G. Alagic (CalTech), “Classical and Quantum 

Circuit Obfuscation,” January 17, 2014.

5. H. Volksmer (University of WisconsinMilwaukee), “Interior and Exterior Harmonics in a 

5-Cyclidic Coordinate System,” January 28, 2014.

6. J. Fish (NYU), “Practical Multiscaling,” February 

12, 2014.

7. A. Makowski (University of Maryland), “On the 

Intersection of Random Graphs with an Application 

to Random Key Pre-Distribution,” February 26, 

2014.

8. K. Sellers (Georgetown University), “A Flexible 

Statistical Control Chart for Dispersed Count 

Data,” March 4, 2014.

9. A. L. Tits (University of Maryland), “Constraint 

Reduction for Linear and Convex Optimization,” 

March 11, 2014.

10. R. Costas-Santos (Universidad de Alcala, Spain), 

“An Overview of Classical Orthogonal 

Polynomials,” March 25, 2014.

11. A. N. Vidyashankar (George Mason University), 

“Dynamical Random Effects Driven Preferential 

 

44 All releases made in role as Tcl Release Manager are available 

from http://sf.net/projects/tcl/files/Tcl/.

Attachment Models,” April 1, 2014.

12. M. Jarret (University of Maryland), “Adiabatic 

Optimization and the Fundamental Gap Theorem,” 

May 27, 2014.

13. D. Katz (Argonne National Labs), “Parallel and 

Distributed Application Paradigms,” May 30, 

2014.

14. S. D. Casey (American University), “The Analysis 

of Periodic Point Processes (Pi, the Primes, 

Periodicities, and Probability),” June 3, 2014.

15. J. Shook (ACMD), “Matrix Scaling: A New 

Heuristic for the Feedback Vertex Set Problem,” 

June 10, 2014.

16. C. Monteleoni (George Washington University), 

“Clustering Algorithms for Streaming and Online 

Settings,” June 17, 2014.

17. M. Mascagni (Florida State University and 

ACMD), “Random Number Generation Using 

Normal Numbers,” June 24, 2014.

18. Y. Kemper (ACMD), “Problems of Enumeration 

and Realizability on Matroids, Simplicial 

Complexes, and Graphs,” August 6, 2014.

19. Y. Baryshnikov (University of Illinois), “On the 

Dimension(s) of the Internet,” August 13, 2014.

20. M. Beck (San Francisco State University), 

“(Enumeration Results for) Signed Graphs,” 

August 28, 2014.

21. H. Edelsbrunner (IST Austria), “Approximation 

and Convergence of the First Intrinsic Volume,” 

September 5, 2014.

22. R. Lehoucq (Sandia National Labs), “A 

Computational Spectral Graph Theory Tutorial,”

September 17, 2014.

Conference Organization

1. H. S. Cohl, Member, Scientific Committee, 13th International Symposium on Orthogonal 

Polynomials, Special Functions, and Applications 

(OPSFA-13), Gaithersburg, MD, June 1-5, 2015.

2. H. S. Cohl, Co-Organizer, Orthogonal Polynomials 

and Special Functions Summer School 6, American 

University, Summer 2016.

3. A. Dienstfrey, Co-Chair, Program Committee, IMA 

Workshop on Uncertainty Quantification for Materials Modeling, (UQ4MM), West Lafayette, IN, 

July 2015.
126 NIST Applied and Computational Mathematics Division

4. G. Doğan, Co-Organizer, Minisymposium on 

Manifolds, Shapes and Topologies in Imaging, 

SIAM Conference on Imaging Science, Hong 

Kong, May 12, 2014.

5. M. Donahue, Co-Organizer, Micromagnetics II 

session, Magnetism and Magnetic Materials 

Conference, Honolulu, HI, November 3-7, 2014.

6. W. Griffin, Publicity Chair, ACM SIGGRAPH 

Symposium on Interactive 3D Graphics and Games 

(I3D), San Francisco, CA, March 14-16, 2014.

7. W. Griffin, Publicity Chair, ACM SIGGRAPH 

Symposium on Interactive 3D Graphics and Games 

(I3D), San Francisco, CA, February 27 – March 1, 

2015.

8. A. Gueye, Co-Organizer, UMD-NIST Workshop on 

Network Science, College Park, MD, January 24, 

2014.

9. F. Hunt, Member, Organizing Committee, Infinite 

Possibilities Conference, Corvallis, OR, March 1-3, 

2015.

10. S. Jordan and Y.-K. Liu, Co-Organizers, UMDNIST Workshop on Quantum Information and 

Computer Science (QuICS), College Park, MD, 

March 31 – April 1, 2014.

11. R. N. Kacker, Co-Organizer, Member Program 

Committee, Third International Workshop on 

Combinatorial Testing (IWCT 2014), Cleveland 

Ohio March 30 - April 2, 2014.

12. P. S. Kuo, Member, Program Committee, CLEO 

Conference, Science & Innovations (S&I) Committee 4: Nonlinear Optical Technologies, San Jose, 

CA, June 8-13, 2014.

13. Y.-K. Liu, Member, Program Committee, 6th International Conference on Post-Quantum 

Cryptography (PQCrypto), Waterloo, Canada, October 1-3, 2014.

14. D. W. Lozier, Co-Chair, Scientific Committee, 13th

International Symposium on Orthogonal Polynomials, Special Functions, and Applications (OPSFA13), Gaithersburg, MD, June 1-5, 2015.

15. M. Mascagni, Co-Organizer, Minisymposium, 

“Monte Carlo Methods for Solving Partial Differential Equations,” Ninth International Congress on 

Industrial and Applied Mathematics (ICIAM),

2015, Beijing, China.

16. M. Mascagni, Member, International Program 

Committee, International Conference on Computational Science (ICCS), Reykjavík, Iceland, June 1-

3, 2015.

17. M. Mascagni, Member, International Program 

Committee for the International Conference on 

Computational Science (ICCS), Cairns, Australia, 

June 10-12, 2014.

18. M. Mascagni, Member, Technical Program Committee, SC14, New Orleans, LA, November 16-21, 

2014.

19. M. Mascagni, Member, Emerging Technology 

Committee, SC14, New Orleans, LA, November 

16-21, 2014.

20. B. R. Miller, Member, Program Committee, Conferences on Intelligent Computer Mathematics, 

University of Coimbra, Portugal, July 7-11, 2014.

21. B. R. Miller, Member, Program Committee, Conferences on Intelligent Computer Mathematics, 

Washington, DC, July 13-17, 2015.

22. B. R. Miller and A. Youssef, Co-Organizers, Conferences on Intelligent Computer Mathematics, 

Washington, DC, July 13-17, 2015.

23. W. F. Mitchell, Member, Scientific Committee, International Conference of Numerical Analysis and 

Applied Mathematics (ICNAAM), Rhodes, Greece, 

September 23-29, 2015.

24. Y. Parker and J. Terrill, Co-Organizers, NIST 

Booth, International Conference for High 

Performance Computing, Networking, Storage and 

Analysis (SC13), Denver, CO, November 18- 21, 

2013. 

25. Y. Parker and J. Terrill, Co-Organizers, NIST 

Booth, International Conference for High 

Performance Computing, Networking, Storage and 

Analysis (SC14), New Orleans, LA, November 17-

20, 2014. 

26. F. A. Potra, Co-Organizer, Nonlinear Programming 

Stream, 20th Conference of the International Federation of Operational Research Societies, Barcelona, 

Spain, July 13-18, 2014. 

27. S. Ressler, Co-Organizer, Web3D Showcase, 

Web3D, Conference, Vancouver Canada, August 

11, 2014. 

28. K. Sayrafian, Member, Technical Program Committee, Symposium on Sensing, Propagation, and 

Wireless Networks for Healthcare Applications, 

Singapore, April 21-24, 2014.

29. K. Sayrafian, Member, Technical Program Committee, 8th International Symposium on Medical 

Information and Communication Technology

(ISMICT 2014), Florence, Italy, April 2-4, 2014.

30. K. Sayrafian, Member, Technical Program Committee, IEEE Symposium on Computer 
Summary of Activities for Fiscal Year 2014 127

Applications and Industrial Electronics (ISCAIE 

2014), Penang, Malaysia, April 7-8, 2014.

31. K. Sayrafian, Member, Technical Program Committee, 8th International Conference on Sensor 

Technologies and Applications (SENSORCOMM 

2014), Lisbon, Portugal, November 16-20, 2014..

32. K. Sayrafian, Member, Technical Program Committee, 4th International Conference on the Internet 

of Things (IoT 2014), Cambridge, MA, October 6-

8, 2014. 

33. K. Sayrafian, Executive and Technical Program 

Committee Co-Chair, 25th IEEE Annual International Symposium on Personal, Indoor and Mobile 

Radio Communications (IEEE PIMRC), Washington, DC, September 2-5, 2014. 

34. B. I. Schneider, Chair, Novel Hardware and Software Paradigms Track, XXVI IUPAP Conference 

on Computational Physics, Boston, MA, August, 

11-14, 2014.

35. X. Tang, Program Committee, Quantum Communications and Quantum Imaging XII (OP415), SPIE 

Optics and Photonics Conference, San Diego, CA, 

August 9-13, 2015.

36. J. Terrill and T. Bednarz, Co-Organizers, Immersive Visualization for Science and Research Birds 

of a Feather (BOF) Session, 41st International Conference and Exhibition on Computer Graphics and 

Interactive Technologies (SIGGRAPH 2014), Vancouver, Canada, August 13, 2014.

Other Professional Activities 

Internal 

1. I. Beichl, Co-Director, ITL Summer Undergraduate 

Research Fellowship (SURF) Program, 2014.

2. R. F. Boisvert, Member, ITL Diversity Committee.

3. R. F. Boisvert, Member, NIST Scientific Computing Steering Group.

4. H. Cohl, Co-Director, ITL Summer Undergraduate 

Research Fellowship (SURF) Program, 2015.

5. A. Dienstfrey, NIST Materials Genome Initiative 

(MGI) Program Committee.

6. A. Dienstfrey, Member, ITL Cyber-Physical Systems Strategic Planning Committee.

7. S. Glancy, Member, NIST Boulder SURF Committee.

8. S. Glancy, Member, ITL Diversity Committee.

9. A. Kearsley, Member, ITL Awards Committee.

10. Y. Kemper, Member, NIST MML-Postdoctoral Association Leadership Committee.

11. K. Sayrafian, Member, ITL Cyber-Physical Systems Strategic Planning Committee.

12. C. Schanzle, Alternate Member, NIST Scientific 

Computing Steering Group.

External 

Editorial

1. I. Beichl, Member, Editorial Board, Computing in 

Science & Engineering.

2. R. F. Boisvert, Associate Editor, ACM Transactions 

on Mathematical Software.

3. R. F. Boisvert, Area Moderator (Numerical Analysis, Mathematical Software, and Computational 

Science, Engineering and Finance), arXiv Computing Research Repository.

4. H. S. Cohl, Guest Editor, Symmetry, Integrability 

and Geometry: Methods and Applications, Special 

Issue on Orthogonal Polynomials, Special Functions and Applications.

5. A. Dienstfrey, Associate Editor, International Journal of Uncertainty Quantification.

6. Z. Gimbutas, Member, Editorial Board, Advances 

in Computational Mathematics.

7. M. Mascagni, Associate Editor, ACM Transactions 

on Mathematical Software.

8. M. Mascagni, Member, Editorial Advisory Board,

Molecular Based Mathematical Biology.

9. M. Mascagni, Member, Editorial Board, Mathematics and Computers in Simulation.

10. M. Mascagni, Member, Editorial Board, Monte 

Carlo Methods and Applications.

11. M. Mascagni, Member, Editorial Board, Advances 

in Computing, Theory and Practice. 

12. W. F. Mitchell, Editor, Journal of Numerical Analysis, Industrial and Applied Mathematics.

13. D. P. O’Leary, Editor-in-Chief, SIAM Journal on 

Matrix Analysis and Applications.

14. D. P. O’Leary, Member, Editorial Board, Education 

Section, SIAM Review.

15. D. P. O’Leary, Member, Editorial Board, SIAM 

Books.

16. D. P. O’Leary, Department Editor, “Your Homework Assignment,” Computing in Science and 

Engineering.
128 NIST Applied and Computational Mathematics Division

17. F. A. Potra, Regional Editor, Americas, Optimization Methods and Software.

18. F. A. Potra, Associate Editor, Journal of Optimization Theory and Applications.

19. F. A. Potra, Associate Editor, Numerical Functional 

Analysis and Optimization.

20. F. A. Potra, Associate Editor, Optimization and Engineering.

21. K. Sayrafian, Associate Editor, International Journal on Wireless Information Networks (IJWIN).

22. K. Sayrafian, Guest Editor, IEEE Communication 

Magazine, Special Issue on “Mobile and Wearable 

BAN.”

23. B. I. Schneider, Member, Editorial Board, Computing in Science & Engineering.

Boards and Committees

1. R. F. Boisvert, Member, International Federation 

for Information Processing (IFIP) Working Group 

2.5 (Numerical Software).

2. R. F. Boisvert, Member, Association for Computing 

Machinery (ACM) Publications Board.

3. R. F. Boisvert, Chair, Association for Computing 

Machinery (ACM) Digital Library Committee.

4. R. F. Boisvert, Member, Member, Reproducibility 

Interest Group45, Research Data Alliance.

5. R.F. Boisvert, Alternate NIST Representative, Subcomittee on the Materials Genome Initiative, 

Committee on Technology, National Science and 

Technology Council.

6. R. F. Boisvert, Member, Program Review Committee, Institute for Defense Analysis (IDA) Center for 

Computing Science.

7. R. F. Boisvert, Member, External Review Panel, 

Department of Computer Sciences, George Washington University.

8. A. Dienstfrey, Member, International Federation 

for Information Processing (IFIP) Working Group 

2.5 (Numerical Software).

9. W. L. George, Member, Argonne National Laboratory, Leadership Computing Facility User Advisory 

Committee. 

10. M. Mascagni, Member, Board of Directors, International Association for Mathematics and Computers 

in Simulation (IMACS).

 

45 https://rd-alliance.org/group/reproducibility-ig.html

11. M. Mascagni, Member, Technical Committee,

Monte Carlo Methods, International Association for 

Mathematics and Computers in Simulation 

(IMACS).

12. M. Mascagni, Member, Peer Review Committee, 

Fulbright Specialist Program, Council for International Exchange of Scholars.

13. G. B. McFadden, Member, SIAM Kleinman Prize 

Selection Committee.

14. G. B. McFadden, Member-at-Large, SIAM Council.

15. B. R. Miller, Member, Math Working Group, 

World Wide Web Consortium (W3C).

16. B. R. Miller, Member, OpenMath Society.

17. D. P. O’Leary, Founding Co-Director, Joint UMDNIST Center for Quantum Information and Computer Science (QuICS).

18. D. P. O'Leary, Member, Oversight Committee, 

Gene Golub SIAM Summer Schools.

19. D. G. Porter, Member, Tcl Core Team.

20. S. Ressler, Member, Web3D Consortium.

21. S. Ressler, Member, Declarative 3D for the Web 

Architecture Community Group, World Wide Web 

Consortium.

22. B. Saunders, Member, Member, Advisory Group, 

NSF CoSMIC Scholars Program, Towson University. 

23. B. Saunders, Member, Business, Industry, and Government (BIG) Committee, Mathematical 

Association of America (MAA).

24. B. Saunders, Webmaster, SIAM Activity Group on 

Orthogonal Polynomials and Special Functions.

25. B. Saunders, Moderator, OP-SF Talk listserv, 

SIAM Activity Group on Orthogonal Polynomials 

and Special Functions.

26. K. Sayrafian, Member, External Advisory Board, 

NIH/NIBIB Quantum Medical Device Interoperability (QMDI) Project.

27. K. Sayrafian, Member, Wireless Medical Technologies Working Group, National Institute of 

Biomedical Imaging and Bioengineering, NIH.

28. B. I. Schneider, Vice-Chair and Chair-Elect, Division of Computational Physics, American Physical 

Society (APS).

29. B. I. Schneider, NIST Representative, Interagency 

Working Group on High End Computing, Federal 
Summary of Activities for Fiscal Year 2014 129

Networking and Information Technology R&D 

Program (NITRD). 

30. B. I. Schneider, Program Committee Chair, Division of Computational Physics, American Physical 

Society. 

31. J. Terrill, NIST Representative, Interagency Working Group on High End Computing, Federal 

Networking and Information Technology R&D 

Program (NITRD). 

Community Outreach

1. B. Alpert, Mentor, Mathematical Modeling in 

Industry, IMA Workshop, University of British 

Columbia, Vancouver, Canada, August 6-15, 2014.

2. F. Hunt, Member, Organizing Committee, Infinite 

Possibilities Conference, Corvallis, OR, March 1-3, 

2015.

3. D. P. O’Leary, Mentor, Mentor Network, Association for Women in Mathematics.

4. M. Mascagni, Visiting Lecturer, Society for Industrial and Applied Mathematics (SIAM).

5. S. Ressler, Distinguished Speaker, Association for 

Computing Machinery (ACM).

6. B. Saunders. Judge (Mathematics), Siemens Competition in Math, Science and Technology, October 

11-15, 2013 in Princeton, NJ. 

7. 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, 2014. 

8. B. Saunders, Panelist, STEM (Science, Technology, Engineering, and Mathematics) Career Panel 

for Middle School Girls, Cora Kelly Recreation 

Center, Alexandria, VA, April 12, 2014.

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 

2013. 

2. B. R. Miller, Member, Ph.D. Thesis Committee, 

Deyan Ginev, Computer Science, Jacobs University, Bremen. Title: Designing Definition Discovery 

– Read, Recognize, Reflect, Repeat.

3. B. R. Miller, Member, Ph.D. Thesis Committee, 

Qun Zhang, Computer Science, George Washington University, Washington DC. Title: MathSimilarity Search (MSS).

4. K. Sayrafian, Member, Ph.D. and M.Sc. Thesis 

Committee, Guanqun Bao, Worcester Polytechnic 

Institute. Title: On Simultaneous Localization and 

Mapping inside the Human Body (Body-SLAM). 

Completed 2014.

5. K. Sayrafian, Member, Ph.D. and M.Sc. Thesis 

Committee, Mehdi Dadfarnia, University of Maryland. Title: Energy Harvesting Microgenerators for 

Medical Body Sensor Network Systems. Completed 

2014.

Awards and Recognition

1. Ronald Boisvert, Fellow, Washington Academy of 

Sciences, May 8, 2014.

2. Ronald Boisvert, Mathematics and Computer Science Award, Washington Academy of Sciences, 

May 8, 2014.

3. Jeffrey Fong, Lifetime Achievement Award, International Conference on Computational Engineering 

and Science (ICCES), Changwon, Korea, June 16, 

2014.

4. Raghu N. Kacker, Silver Medal (joint award), Department of Commerce, December 10, 2014.

5. Emanuel Knill, Arthur S. Flemming Award, George 

Washington University, June 9, 2014.

6. Bruce R. Miller, Outstanding Contribution to ITL, 

NIST Information Technology Laboratory, August 

19, 2014.

7. 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.

8. Kamran Sayrafian, Embassy Science Fellow, U.S. 

Department of State, July 2014.

9. Christopher Schanzle, Outstanding Service Award, 

NIST Chapter of Sigma Xi, June 5, 2014.

10. Christopher Schanzle, Outstanding Technical Support (joint award), NIST Information Technology 

Laboratory, August 19, 2014.

11. Y. Zhang, Scott Glancy and Emanuel Knill, Outstanding Journal Paper, NIST Information 

Technology Laboratory, August 19, 2014.
130 NIST Applied and Computational Mathematics Division

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. Theiss Research46: Quantum Memories for Longdistance Quantum Communications, $420,821 (3 

years). PI: Dr. Lijun Ma.

2. University of Maryland, College Park, MD: Network Science Approach to Interdependent Security,

$70,590 (3 years). PI: Prof. Richard La.

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

Automation Apps

The Boeing Company

Cadence Design Systems

Centre Suisse d'Electronique et Microtechnique ‒ 

CSEM (Switzerland)

Foray Technologies

Fraunhoffer

Gener8 

HRL Laboratories

IBM Research

Lockheed Martin

Mechdyne

Microsoft

Northrop-Grumman

Raytheon/BBN

Schwarz Forensic Enterprises

SIKA Technology A.G. (Switzerland)

Tata Research Development and Design Centre (India)

Government/Non-profit Organizations

Air Force Office of Scientific Research

Argonne National Laboratory

Army Research Laboratory

Army Research Office

Association for Computing Machinery ‒ ACM

National Metrology Center ‒ CENAM (Mexico)

Center for Integration of Medicine and Innovative 

Technology ‒ CIMIT

 

46 http://www.theissresearch.org/

Center for Research and Advanced Studies of the National Polytechnic Institute ‒ CINVESTAV 

(Mexico)

China Special Equipment Inspection and Research Institute, Beijing (China)

The Commonwealth Scientific and Industrial Research 

Organisation ‒ CSIRO (Australia)

Department of Energy

Electric Power Research Institute

European Commission Joint Research Center

Food and Drug Administration

Institute for Defense Analysis Center for Computing 

Sciences

Indian Statistical Institute (India)

Institute for Mathematics and its Applications

Institute of Physics and Chemistry of Materials ‒ 

PCMS, National Center for Scientific Research ‒ 

CNRS (France)

International Federation for Information Processing ‒ 

IFIP

Johns Hopkins University Applied Physics Lab

Korea Research Institute of Standards and Science

Lawrence Livermore National Laboratory

Mathematisches Forschungsinstitut Oberwolfach (Germany)

MIT Lincoln Labs

Montgomery County Maryland

NASA Glenn Research Center

NASA Independent Verification and Validation Facility

National Center for Atmospheric Research ‒ NCAR

National Institute of Biomedical Imaging and Bioengineering

National Institutes of Health

National Institute of Science Education and Research 

(India)

National Physical Laboratory (UK)

National Renewable Energy Laboratory ‒ NREL

National Science Foundation

National Oceanographic and Atmospheric Administration

Noblis

Nuclear Regulatory Commission

Oak Ridge National Laboratory

Open Math Society

Pacific Northwest National Laboratory

Poolesville High School, Montgomery County, MD

Princeton Plasma Physics Laboratory

Sandia National Laboratories

Smithsonian Institution Digitization Program Office

Society for Industrial and Applied Mathematics ‒ 

SIAM

Southwest Research Institute

Theiss Research

US Air Force, Eglin Air Force Base
Summary of Activities for Fiscal Year 2014 131

World Wide Web Consortium 

Web3D Consortium

Universities

American University

Beijing Institute of Technology, Beijing (China)

Bowie State University

Brown University

California Institute of Technology

Carnegie Mellon University

China University of Petroleum (China)

City University of Hong Kong (China)

City University of New York

Concordia University, Montreal, Canada

Dalian University of Technology (China)

Dartmouth College

East China University of Science and Technology 

(China)

Federal University of Rio Grande do Norte (Brazil)

Florida State University

George Mason University

George Washington University

Georgetown University

Harvard University

Harvey Mudd College

Hood College

Howard University

Iowa State University

Imperial College, London (UK)

Indian Institute of Technology

Indiana University

Istituto per le Applicazioni del Calcolo (Italy)

Jackson State University

Jacobs University Bremen (Germany)

Kiel University (Germany)

Kings College London (UK)

Lanzhou University of Technology (China)

Louisiana State University

Lund University (Sweden)

Macquarie University (Australia)

Millersville University of Pennsylvania

Nanyang University (Singapore)

National Institute of Technology (India)

National University of Singapore (Singapore)

Ningbo University (China)

Northwestern University

New York University

Oslo University (Norway)

Ozyegin University (Turkey)

Pierre and Marie Curie University (France)

Polytechnic University of Puerto Rico

Princeton University

Purdue University

Rice University

Rochester Institute of Technology

Shandong University (China)

Smith College

Saint Olaf College

Stanford University

State University of New York at Binghamton

Swarthmore College

Texas A&M University

The College of New Jersey

Three Gorges University (China)

Tohoko University (Japan)

Towson University

Tsinghua University (China)

Tulane University

Tufts University

Ulm University (Germany)

Uniformed Services University of the Health Sciences

University at Albany

University of Alcalá (Spain)

University of Antwerp (Belgium)

University of Arizona

University of Bordeaux (France)

University of Bergamo (Italy)

University of British Columbia (Canada)

University of California at Berkeley

University of California at Davis

University of California at Irvine

University of California at San Diego

University of California at Santa Barbara

University of Campinas (Brazil)

University of Colorado at Boulder

University of Colorado at Denver

University of Copenhagen (Denmark)

University of the District of Columbia

University of Göttingen (Germany)

University of Hong Kong (China)

University of Houston

University of Illinois at Urbana-Champaign

University of Lisbon (Portugal)

University of Maryland Baltimore County

University of Maryland College Park

University of Maryland University College

University of Miami

University of Michigan

University of Montreal (Canada)

University of Northern Texas

University of Oklahoma

University of Oulu (Finland)

University of South Carolina

University of Surrey (UK)

University of Technology Sidney (Australia)

University of Texas at Arlington

University of Texas at Dallas

University of Toronto

University of Waterloo (Canada)

University of Wisconsin Milwaukee

University of Zagreb (Croatia)

Virginia Polytechnic Institute and State University

Washington University

Waterloo University
132 NIST Applied and Computational Mathematics Division

Worcester Polytechnic University

Yale University

Yokohama National University (Japan)
Summary of Activities for Fiscal Year 2014 133

Part V: Appendix

 Part V

Appendix
134 NIST Applied and Computational Mathematics Division
Summary of Activities for Fiscal Year 2014 135

Staff

ACMD consists of full time permanent staff located at NIST laboratories in Gaithersburg, MD and Boulder, 

CO. This is supplemented with a variety of special appointments. The following list reflects all appointments held during any portion of the reporting period (October 2013 – December 2014). For students and 

interns, see Staff News on page 8. (*) 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.

Robert Bohn, Ph.D. (Physical Chemistry), University of Virginia, 1991

Alfred Carasso, Ph.D. (Mathematics), University of Wisconsin, 1968

Roldan Pozo, Ph.D. (Computer Science), University of Colorado at Boulder, 1991

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

Bert Rust, Ph.D. (Astronomy), University of Illinois at Urbana-Champaign, 1974

NRC Postdoctoral Associates

Sean Colbert-Kelly, Ph.D. (Mathematics), Purdue University, 2012

Michael Cromer, Ph.D. (Applied Mathematics), University of Delaware, 2011

 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)

Mirit Aladjem, Ph.D. / National Institutes of Health

James Benson, Ph.D. / Northern Illinois University

David Cotrell, Ph.D. / CD-Adapco

*John Gary, Ph.D. / NIST (retired)

David Gilsinn, Ph.D. / NIST (retired)

Daniel Kaslovsky, Ph.D. / University of Colorado

Yu (Jeff) Lei, Ph.D. / University of Texas at Arlington

P. Aaron Lott, Ph.D. / Lawrence Livermore National Laboratory

Itzel Dominquez Mendoza / Centro Nacional de Metrología, Mexico

Bruce Murray, Ph.D. / SUNY Binghamton
136 NIST Applied and Computational Mathematics Division

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

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

Contractors (Name, Degree / Home Institution)

Qiming Wang / Dakota Consulting

Guest Researchers (Name, Degree / Home Institution)

Gunay Dogan, Ph.D. / Theiss Research

Adri Olde Daalhuis, Ph.D. / University of Edinburgh

Tamara Kolda, Ph.D. / Sandia Laboratories, Livermore

Leonard Maximon, Ph.D. / George Washington University

Computing and Communications Theory Group

Ronald Boisvert, Acting Leader

 Isabel Beichl, Project Leader, Ph.D. (Mathematics), Cornell University, 1981 

Brian Cloteaux, Ph.D. (Computer Science), New Mexico State University, 2007

*Scott Glancy, Ph.D. (Physics), University of Notre Dame, 2003

Barry Hershman, A.A. (Electronics Engineering), Capitol College, 1979

Stephen Jordan, Ph.D. (Physics), Massachusetts Institute of Technology, 2008

 *Emanuel Knill, NIST Fellow, Ph.D. (Mathematics), University of Colorado at Boulder, 1991

Paulina Kuo, Ph.D. (Physics), Stanford University, 2008

 Yi-Kai Liu, Ph.D. (Computer Science), University of California, San Diego, 2007

 Vladimir Marbukh, Ph.D. (Mathematics) Leningrad Polytechnic University, 1986

James Shook, Ph.D. (Mathematics), University of Mississippi, 2010

Oliver Slattery, M.S. (Electrical Engineering), Johns Hopkins University, 2008

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
Summary of Activities for Fiscal Year 2014 137

Guest Researchers (Name, Degree / Home Institution)

*Bryan Eastin, PhD. / 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

Amada Streib, Ph.D. / IDA Center for Computing Sciences

Noah Streib, Ph.D. / IDA Center for Computing Sciences

High Performance Computing and Visualization Group

Judith Terrill, Leader, Ph.D. (Information Technology), George Mason University, 1998 

Yolanda Parker, Office Manager

William George, Ph.D. (Computer/Computational Science), Clemson University, 1995

Terence Griffin, B.S. (Mathematics), St. Mary’s College of Maryland, 1987

Wesley Griffin, M.S. (Computer Science), University of Maryland Baltimore County, 2010

John Hagedorn, M.S. (Mathematics), Rutgers University, 1980

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
138 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

AMS American Mathematical Society

arXiv preprint archive housed at Cornell University (http://arxiv.org/)

AS autonomous system

ASCE American Society of Civil Engineers

ASTM ASTM International, formerly known as the American Society for Testing and Materials

BAN body area network

BD Blitzstein-Diaconis

BMG bulk metallic glasses

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

CCS IDA Center for Computing Sciences

CDF cumulative distribution function

CFPG Coulomb force parametric generator

CI configuration interaction

CINVESTAV Center for Research and Advanced Studies of the National Polytechnic Institute (Mexico)

CMA University of Antwerp Computational Mathematics Research Group

CNRS Centre National de la Recherche Scientifique (France)

CNST NIST Center for Nanoscale Science and Technology

CPA cryoprotective agent

CPS cyber-physical system

CPU central processing unit

CT combinatorial testing

CT computed tomography

CTL NIST Communications Technology Laboratory

CY calendar year

DIM diffuse interface model

DLMF Digital Library of Mathematical Functions

DMI Dzyaloshinskii-Moriya interaction

DNA deoxyribonucleic acid

DOAS dual optical absorption spectroscopy

DOE U.S. Department of Energy

DPD dissipative particle dynamics

DRMF digital repository of mathematical functions

EC error correction

EH energy harvesting

EIT electromagnetically induced transparency

EL NIST Engineering Laboratory

EBSD electron backscatter data

ESPCI École Supérieure de Physique et Chimie Industrielles de la Ville de Paris (France)

ETSI European Telecommunications Standards Institute

FCU fan coil unity

FEDVR finite element discrete variable method

FEM finite element method

FFT fast Fourier transform

FPGA field-programmable gate array

FVS feedback vertex set
Summary of Activities for Fiscal Year 2014 139

FWM four-wave mixing

FY fiscal year

GAMS Guide to Available Mathematical Software

GF(2) Galois field of two elements

GPS Geographic Positioning System

GPU graphics processing units

GSSM greenhouse gas sequestration monitoring

GUI graphical user interface

HIM helium ion microscope

HPCVG ACMD High Performance Computing and Visualization Group

HTML hypertext markup language

HVAC heating, ventilation and air conditioning

HVACSIM+ simulation testbed for HVAC systems

Hy-CI Hylleraas-Configuration Interaction technique

ICCES International Conference on Computational Engineering and Science

ICERM Institute for Computational & Experimental Research in Mathematics (Brown University)

IDA Institute for Defense Analysis

IDEA IRIS Development Environment for Applications

IDS interdependent security

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

INCITE Innovative and Novel Computational Impact on Theory and Experiment (DOE Program)

IRIS Interpreted Runtime Immersive Scenegraph

ISGG International Society for Grid Generation

ISIMA Institut Supérieur d’Informatique, de Modélisation et de leurs Applications (France)

ISO International Organization for Standardization

IT information technology

ITL NIST Information Technology Laboratory

ITS NTIA Instritute for Telecommunication Sciences

IVE immersive visualization environment

IVF in vitro fertilization

JILA joint NIST-University of Colorado physics research institute

KLS Koekoek, Lesky and Swarttouw

LaTeX a math-oriented text processing system

LaTeXML LaTeX to MathML translator

LDPC low density parity check

LiDAR light detection and ranging

LOCC local operations and classical communication

LR local realism

LTE long-term evolution

MAA Mathematical Association of America

MALDI-RTOF matrix-assisted laser desorption ionization reflectron time-of-flight (mass spectrometer)

MALDI/TOF matrix-assisted laser desorption/ionization time-of-flight (mass spectrometer)

MathML Mathematical Markup Language (W3C standard)

MD molecular dynamics

MDPC moderate density parity check

MEMS micro-electro-mechanical system

MGI Materials Genome Initiative

MIA minimum interference allocation

MIT Massachusetts Institute of Technology

MKM mathematical knowledge management

MML NIST Material Measurement Laboratory

MPEG7 multimedia content description standard

MPI Message Passing Interface
140 NIST Applied and Computational Mathematics Division

MRAM magneto-resistive random access memory

MRI magnetic resonance imaging

MSE mean squared error

muMAG Micromagnetic Activity Group

NASA National Aeronautics and Space Administration

NBS National Bureau of Standards

NCAR National Center for Atmospheric Research

ND nano-diamond

NDE non-destructive evaluation

NIH National Institutes of Health

NIST National Institute of Standards and Technology

NISTIR NIST Internal Report

NITRD Networking and Information Technology Research and Development

NMR nuclear magnetic resonance

NPSC National Physical Science Consortium

NRC National Research Council

NRC US Nuclear Regulatory Commission

NSA National Security Agency

NSF National Science Foundation

NTIA National Telecommunications and Information Administration

NUREG US Nuclear Regulatory Commission

NV nitrogen vacancy

NVD National Vulnerability Database

NYU New York University

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)

PID proportional integral derivative

PML NIST Physical Measurement Laboratory

PPLN periodically poled lithium niobate

PREP Professional Research Experience Program

PSCR NTIA Public Safety Communications Research

PSNR peak signal-to-noise ratio

QD quantum dot

QDPD quarternion-based dissipative particle dynamics

QKD quantum key distribution

QuICS UMD-NIST Joint Center for Quantum Information and Computer Science

R&D research and development

RF radio frequency

SBIR Small Business Innovative Research

SCGM scaled conjugate gradient method

SDE stochastic differential equation

SED ITL Statistical Engineering Division

SEM scanning electron microscope

SHIP NIST Summer High School Internship Program

SIAM Society for Industrial and Applied Mathematics

SIGACT ACM Special Interest Group in Algorithms and Computation Theory

SIGGRAPH ACM Special Interest Group on Graphics

SIR signal-to-interference ratio

SIS sequential importance sampling

SiV silicon vacancy

SPDC spontaneous parametric down-conversion

SPIE International Society for Optical Engineering

SPL software product line
Summary of Activities for Fiscal Year 2014 141

SRM standard reference material

SUNY State University of New York

SURF Student Undergraduate Research Fellowship

SVG scalable vector graphics

TES transition edge sensor

TSCM truncated singular components method

TV total variation

UK United Kingdom

UMBC University of Maryland Baltimore County

UMD University of Maryland

UMIACS University of Maryland Institute for Advanced Computer Studies

UQ uncertainty quantification

USGS US Geological Survey

VR virtual reality

VRML virtual reality modeling language

W3C World Wide Web Consortium

WAS Washington Academy of Sciences

WebGL Web-based Graphics Library

WUSTL Washington University St. Louis

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