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An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993 (1994)

Chapter: 11 COMPUTING AND APPLIED MATHEMATICS LABORATORY

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Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

11

Computing and Applied Mathematics Laboratory

PANEL MEMBERS

Gary C. McDonald, General Motors NAO Research and Development Center, Chair

Ralph Z. Roskies, University of Pittsburgh, Vice Chair

Marc A. Berger, Georgia Institute of Technology

Mary Ellen Bock, Purdue University

Allen L. Brown, Jr., Xerox Corporation

Avner Friedman, University of Minnesota

Dieter Fuss, Lawrence Livermore National Laboratory

Carl M. Harris, George Mason University

John Hopcroft, Cornell University

Andrew M. Odlyzko, AT&T Bell Laboratories

Robert E. O'Malley, Jr., University of Washington

Jerome Sacks, National Institute of Statistical Sciences

David F. Shanno, Rutgers University

Daniel L. Solomon, North Carolina State University

Norman K. Sondheimer, General Electric Corporate Research and Development

Ivar Stakgold, University of Delaware

Robert G. Voigt, National Science Foundation

Submitted for the panel by its Chair, Gary C. McDonald, this assessment of the fiscal year 1993 activities of the Computing and Applied Mathematics Laboratory is based on a site visit by and meeting of the panel on May 10-12, 1993, and on the annual report of the laboratory.

LABORATORY OVERVIEW
Mission and Objectives

The Computing and Applied Mathematics Laboratory (CAML) ensures (1) that the best methods and tools of modern applied mathematics, statistics, and scientific computing are made available for use by NIST scientists and engineers and by their collaborators in industry, government, and research institutions and (2) that a modern computing, communications, and data management environment is developed and maintained for scientific and administrative applications. CAML differs from other NIST major laboratories in that its primary purpose is to provide services to the other NIST laboratories, in contrast to providing services for use external to NIST. Thus, CAML must keep well informed and sensitive to the needs of other organizational entities within NIST for hardware and software, scientific and

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

technical support, and advice on current developments in mathematics, computing, and telecommunications.

Strategy

CAML's strategic plans (as presented in the annual briefing reports of CAML and its divisions and offices prepared for the fiscal year 1993 site visit) provided an overview of CAML's objectives. In some instances, the detail was insufficient to allow for full assessment. For example, CAML's Strategic Plan for NIST for Computing and Communications (NIST, February 1993) had clear objectives and schedules for providing upgrades and extensions to central computing services; however, budgetary support was not clear. In contrast, the manufacturing application component of the National Information Infrastructure initiative for fiscal year 1995 included both implementation and budgetary details.

The Statistical Engineering Division's strategic plan outlined important objectives and projects to be carried out in collaboration with other NIST laboratories but did not address funding options.

The Applied and Computational Mathematics Division (ACMD) did not provide a separate strategic plan. ACMD's planning information in CAML's Description of the Laboratory and Its Operations (May 1993) was inadequate for assessment purposes. For example, the acquisition of an instrument for massive parallel processing, the Paragon from Intel Corporation, by NIST's Computer Systems Laboratory could provide ACMD with an opportunity for experience with scalable parallel processing; however, the panel saw no ACMD plans for research using the Paragon for simulating physical problems.

CAML is in an awkward position. The Strategic Plan for NIST for Computing and Communications (NIST, February 1993) states under “Critical Issues” (p. 14) that “the NIST scientific program is entering a very dynamic period which may well lead to significant program expansion and changes of emphasis. . . .” These program expansions and changes are based on major federal initiatives such as the multiagency HPCC program (first described in the High-Performance Computing Act of 1991 and again in the Information Infrastructure and Technology Act of 1993). However, CAML's funding level has not been set. Clearly, waiting for funding assurance to add critical staff will not achieve the timely results anticipated nationally. Parenthetically, the panel is not certain that current staff are working on problems of highest strategic priority.

If funding materializes along with opportunities to collaborate with other laboratories within NIST and with external organizations, projects could proceed simultaneously with staff buildup. To retain CAML' s scientific integrity, partnerships must be based on true intellectual collaboration. Timely response to opportunities and adaptability to new projects and

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

directions pose major challenges to CAML. As NIST changes its priorities and its criteria for program success in keeping with its expanded mission, CAML's traditional approaches to managing services within NIST may no longer be relevant.

Organization

The Computing and Applied Mathematics Laboratory's organization is shown in Figure 11.1.

Resources

Outlined in Table 11.1 and Table 11.2 are the Computing and Applied Mathematics Laboratory's funding and the size and distribution of its staff.

CAML's staff skills are submarginal for fulfilling its potential role in NIST's expanded mission. Should CAML have the opportunity to seek critically needed new competencies, its salary restrictions may to some extent limit recruitment options; however, CAML has access to talent through external collaboration and development of additional in-house skills.

CSL has space issues: (1) The serious shortage of rooms assigned to CAML makes it difficult to find offices for visitors and recruitment. (2) CAML staff has been and will continue to be dispersed. CAML' s former quarters in the Administration Building are being taken over by other NIST units, and CAML's divisions are being moved to various campus locations. Collaboration between the Statistical Engineering Division staff and the Office of Applied Economics staff, for example, will undoubtedly be adversely affected by the impending move of the Office of Applied Economics that will leave it and the Statistical Engineering Division at opposite ends of NIST's Gaithersburg campus.

CAML'S RESPONSES TO FISCAL YEAR 1992 RECOMMENDATIONS

In its fiscal year 1992 assessment report (p. 277), the panel recommended that CAML's divisions develop strategic plans based on consultation with their staff. In response, the Strategic Plan, NIST Statistical Engineering Division (May 1993), was drafted based on nine strategic elements selected by the division's staff members. The overall strategy statement, with an emphasis on service to selected clients, seemed appropriate. Strategic Plan for NIST Computing and Communications (NIST, February 1993), prepared by CAML as background data for the panel's program review, was based on an upgraded level of computing facilities and stressed the future for improvements in NIST's computing environment arising from technological trends. The trends in NIST 's requirements for computing services were also described, as were NIST's major computing issues.

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

FIGURE 11.1 Organization and structure of the Computing and Applied Mathematics Laboratory.

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

TABLE 11.1 Fiscal Year 1993 Budget Estimates ($ Million) for the Computing and Applied Mathematics Laboratory

Source/Category

$ Million

Percentage of Total

Resources

   

STRS/ITSa

19.88

62.65

Other agency

3.86

12.17

NIST overhead

7.56

23.83

Other

0.43

1.36

Total

31.73

100.00

Expenditures

   

Labor

18.60

58.62

Other objects

13.13

41.38

Total

31.73

100.00

Depreciable equipment

1.00

 

a Scientific and Technical Research and Services (i.e., direct appropriations for CAML's internal research) /Industrial Technical Services (i.e., appropriations for CAML's extramural services)

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

TABLE 11.2 Computing and Applied Mathematics Laboratory (CAML) Staff Count as of May 2, 1993--Each Site and Laboratory Total

 

Staff Type

 

Site and Category

ES/STa

ZPb

ZTc

ZAd

ZSe

Total

Boulder

           

Full-time permanent

 

25

 

4

6

35

Postdoctoral

 

1

     

1

Part-time permanent

 

1

   

2

3

Intermittent

 

4

     

4

Guest researchers

 

1

     

1

Subtotal (Boulder)

 

32

 

4

8

44

Gaithersburg

           

Full-time permanent

8

105

3

8

19

143

Postdoctoral

 

1

     

1

Part-time permanent

 

7

 

1

3

11

Intermittent

 

24

   

2

26

Guest researchers

 

14

     

14

Subtotal (Gaithersburg)

8

151

3

9

24

195

CAML (Boulder, Gaithersburg)

           

Full-time permanent

8

130

3

12

25

178

Postdoctoral

 

2

     

2

Part-time permanent

 

8

 

1

5

14

Intermittent

 

28

   

2

30

Guest researchers

 

15

     

15

Total CAML Staff

8

183

3

13

32

239

a Senior Executives/NIST Fellows

b Professional

c Technical

d Administrative

e Support

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

Plans for the Applied and Computational Mathematics Division were incorporated in CAML's “Description of the Laboratory and Its Operations ” (May 1993) also prepared for the panel meeting. The panel would have preferred to review a stand-alone strategic plan for the division. After describing CAML's plans and valuable ongoing work, CAML concluded (p. 36) that “. . . it is not possible to request a major initiative in applied and computational mathematics.” The panel sees no indication that this condition will change soon.

In response to this panel's recommendations in fiscal year 1992, NIST's director called for a proposal for a mathematics-based manufacturing initiative involving the Manufacturing Engineering Laboratory, the Building and Fire Research Laboratory, and CAML. NIST's director deemed the resulting proposal too general to justify funding. Nevertheless, the panel suspects that interactions among the NIST laboratories participating in preparing the proposal may yet bear fruit.

NIST is proposing budget initiatives for HPCC and Advanced Materials and Processing, initiatives that are highly visible nationally and involve CAML collaboration with other NIST laboratories. Also, CAML is proposing to support initiatives in virtual design technology, biotechnology and chemical process design, and molecular engineering. However, CAML does not have the staff to adequately carry out these worthwhile initiatives.

The panel recommended in 1992 that the Statistical Engineering Division recruit senior staff with industrial expertise to support initiatives in advanced manufacturing and industrial-related ventures. The search was unsuccessful (due in part to salary constraints).

As recommended by the panel in 1992, the Computer Services Division instituted a more proactive management of the Cray Y-MP. Performance rates of 80 Mflops are now typical. Doubling of the Cray's memory to 32 megawords was in order, as was the removal rather than the upgrade of the CONVEX C120. Use of the visualization laboratory has increased such that staff size is the limiting factor.

PANEL'S MAJOR FINDINGS, CONCLUSIONS, AND RECOMMENDATIONS--FISCAL YEAR 1993
Findings and Conclusions
  • A vigorous Computing and Applied Mathematics Laboratory is critical to the NIST mission to improve U.S. industrial competitiveness. As industry continues to move toward mathematics-based approaches to product and process design, engineering, and manufacturing, CAML could contribute critical mathematics and statistics to industrial-related initiatives.

  • In keeping with NIST's expanding mission, CAML must become more proactive, seizing opportunities for leadership in the development of emerging technology as well as providing

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

services for other NIST programs. CAML should develop scenarios for alternate budget contingencies and identify priorities and partnerships under each scenario that are compatible with CAML's expertise and recruiting capabilities.

  • Almost all of CAML's planning emphasizes that staff size and breadth of expertise limit the laboratory's goals. Apparently, CAML believes there is not much more that can be done without an increase in staff.

Recommendations
  1. CAML should formulate initiatives for assuming national leadership in the development and dissemination of generic technology. Promising technology assistance includes modeling in materials science, mathematics-based approaches to manufacturing (including both the mathematical basis and experimental design), the harnessing of computer workstation power, and dissemination of advanced reference information such as CAML's Guide to Available Mathematical Software.

    To assume additional national leadership roles CAML should identify additional skills needed as a guide to recruiting and building competencies in a timely fashion. For example, skills are needed in multivariate methods, stochastic processes, and time series. Unless unforeseen resources are made available, CAML should be selective in making commitments for contributions to the federal multiagency High Performance Computing and Communications program in order not to limit its potential for contributions to other NIST initiatives also of national import.

  2. CAML should strengthen its direct linkage with industry by, e.g., assigning CAML professionals to industrial sites, participating in technical reinvestment projects, entering Cooperative Research and Development Agreements, and detailing professional staff to the Advanced Technology Program.

  3. CAML should expand the American Statistical Association-NIST-National Science Foundation Fellowship Program to create additional leadership in applied mathematics and computing.

  4. CAML should identify, encourage, and reward team efforts with counterparts in other CAML divisions and other NIST laboratories. For example, a joint initiative in mathematics-based product design would involve collaboration in computational geometry, adaptive mesh generation, physical modeling, mathematical optimization, and statistical design. Individual initiatives that abound within CAML should be integrated to achieve maximum impact.

  5. CAML should charge a task force including non-CAML participants with implementing the above recommendations. Recommendations should be sought from scientists in other NIST units and external constituencies.

  6. CAML divisions should (a) develop strategic plans that appraise the prospects for funding from other agencies, from other parts of NIST, and from allocations for base programs,

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

i.e., Scientific and Technical Research and Services as appropriated directly from Congress and (b) develop programmatic priorities based on these plans in the course of periodic division meetings.

  1. CAML should join with other NIST laboratories in again exploring the desirability and feasibility of a NIST initiative addressing mathematics-based manufacturing generic technology.

  2. CAML should assign priorities and schedule dates for upgrading NIST's computer and communications hardware and services; i.e., CAML should evolve a living document of planned improvements that is readily available for planning purposes to NIST's other organizational units as well as CAML's staff.

  3. The Applied and Computational Mathematics Division should be more proactive, asserting its potential for important contributions to the long-range strategies of CAML and in turn NIST. For example, the division should, through collaboration with NIST's Materials Science and Engineering Laboratory, vigorously pursue the establishment of a Materials Theory Center.

  4. The Statistical Engineering Division should continue to recruit for industrial experience and expose senior staff to industrial practices.

ASSESSMENT OF DIVISION PROGRAMS
Statistical Engineering Division

The Statistical Engineering Division's comprehensive strategic plan, based on input from the division staff, responds to the needs of nine client groups. In its fiscal year 1992 assessment, the panel called for strategic planning to “focus on the extent to which staff and management wish to emphasize the historical consultative role and the extent to which they wish to strike out in pursuit of new initiatives” (p. 277). The division 's plan is heavily shaped by “individual values and capabilities, budget constraints, management expectations, tasking from external clients (the Congress), recommendations of assessment panels, requests from internal clients, and changing technology. These constraints are real; however, the challenge remains for staff members to promote their own vision for the division.

The Statistical Engineering Division's staff received a Department of Commerce Silver Medal; published in more than 60 referred journals and conference proceedings; made 40 technical presentations at professional meetings, universities, and other institutions; and participated in an impressive array of editorial and professional activities. The division's tutorial intramural courses in statistics for other NIST scientists and engineers continue to be in demand.

Of special note are the division's successful workshops for industry, including two in the design of experiments and one each in electrical measurement assurance and accelerated-life testing,

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

as well as a conference on extreme values. As points of direct contact with industrial firm such as SAS, Xerox Corporation, General Motors Corporation, and Ford Motor Company, and as important vehicles for the transfer of technology, the Statistical Engineering Division 's workshops are thus central to NIST's mission.

Workshops and the Manufacturing Technology Centers offer avenues for broadening the division's collaboration with industry, as would visits of Statistical Engineering Division scientists to industrial sites for extended periods.

The panel notes the success of the American Statistical Association-NIST-National Science Foundation Fellowship Program in bringing senior scientists tothe division, complementing Statistical Engineering Division expertise in areas such as life-testing, multivariate methods, and Bayesian analysis, and leading to very successful workshops for industry. The fellowship program thus enables an effective and visible interchange between industry and division researchers.

The ongoing effort to hire a senior statistics researcher with manufacturing experience has not borne results, partly because the experience requirements and limited salary appear incompatible. Although excellent junior scientists from topflight institutions have been hired, additional senior research leadership is needed. For example, additional competence is needed in multivariate methods (especially multivariate process control), stochastic processes, and time series (in collaborative electronics research).

Recommendation

The Statistical Engineering Division's two-fold mission, involving basic research in statistical science and collaboration with other NIST scientists, should be broadened to include extensive and direct collaboration with industry.

Applied and Computational Mathematics Division

The Applied and Computational Mathematics Division's research is of high quality, attracts national interest, and is relevant to NIST's mission.

The division's study of materials solidification (involving a blend of modeling, computation, and basic physics) benefits from well-established working relationships among metallurgists and applied mathematicians at NIST, at leading universities, and in industry. The division's broader research in materials science modeling has national importance, recognition, and promise, and it supports mathematics-based manufacturing.

The division's Guide to Available Mathematical Software continues to be a very visible part of the division's activity and is the division's major contribution to NIST's participation

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

in the federal HPCC initiative. The division will need an additional staff member to provide Guide services for the HPCC initiative. Further extension of the Guide presents difficulties that must be dealt with in a timely fashion. In the panel's fiscal year 1992 report (p. 273), the panel suggested that CAML could either attempt to attract an industrial partner to support the Guide's implementation as a product or use the Guide as a research tool. Attracting an industrial partner remains an attractive option. The Guide also presents several other opportunities. For example, the Guide's support for access to available mathematical software information could be broadened, thereby positioning CAML for a role in the National Information Infrastructure program. As mentioned in the fiscal year 1992 report, artificial intelligence could be used to support the novice user.

NIST's current proposal for an initiative in manufacturing offers an opportunity and challenge to the Applied and Computational Mathematics Division. Aggressive marketing of the role of applied and computational mathematics in contemporary manufacturing and management would be consonant with the call made elsewhere (see, e.g., Avner Friedman, James Glimm, and John Lavery, The Mathematical and Computational Sciences in Emerging Manufacturing Technologies and Management Practices, Society for Industrial and Applied Mathematics, Philadelphia, 1992) for raising the public' s consciousness of the industrial relevance of mathematics. Preliminary attempts at marketing have been made; however, a longer-term demonstration of the relevance of mathematics to manufacturing, possibly through NIST's Manufacturing Engineering Laboratory, would be most effective. Any demonstration of the relevance of mathematics to modern manufacturing would include applied probability (queueing theory, discrete event simulation, quality assurance), computational and combinatorial optimization, and discrete mathematics. In addition to providing a stronger raison d'être for supporting applied mathematics at NIST, a successful collaboration in manufacturing would provide a springboard for additional collaboration with other groups within NIST and external to NIST.

Recommendation

The Applied and Computational Mathematics Division should seek more collaborations with other NIST laboratories as well as with extramural partners and focus on a small number of carefully selected options to best serve the needs of NIST and the scientific community at large.

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Office of Applied Economics

CAML's office of Applied Economics conducts research for and provides technical assistance to other organizations within NIST, conducts prototype training programs for NIST's scientists and engineers, and responds to congressional mandates for special microeconomic analyses. To help government and industry better allocate their resources, the office develops benefit-cost analyses, life-cycle costing, multicriteria decision analyses, risk analyses, and econometric analyses to indicate economically efficient choices among new technologies, processes, government programs, legislation, codes, and standards. The office consists of a chief, part-time secretary, and four professionals.

The largely interagency funding of Office of Applied Economics projects limits or at least prescribes the staff's opportunities for presentations and publications. The office's contributions to NIST programs, such as those in the Building and Fire Research Laboratory and the Manufacturing Engineering Laboratory, and to Advanced Technology Program efforts are unique and are particularly supportive of NIST's expanded mission. The office makes multiple use of the competences throughout CAML for its studies and economic model building.

Recommendation

The CAML should review the potential of the Office of Applied Economics in the context of NIST's expanding mission.

NIST Central Computing and Communications

As implied in the above mission statement for the Computing and Applied Mathematics Laboratory, CAML provides NIST with central scientific computing services and software, voice and data communications, administrative computing services, and related scientific and technical support. To fulfill this responsibility, CAML emphasizes NIST's effective use of current computing and telecommunications resources; the development and implementation of modern central and local computing environments; and the analysis, planning for, and acquisition of improved and expanded resources to meet critical future needs of NIST's scientists, engineers, and administrators.

CAML has four divisions dedicated to developing and managing NIST 's central computing and communication services. CAML's Scientific Computing Environments Division is responsible for scientific visualization, user training, and software administration and support; CAML's Computer Services Division improves, operates, and administers NIST's central computing resources; CAML's Computer Systems and Communications Division oversees NIST 's central networking, telecommunications services,

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×

and major system acquisition; and CAML's Information Systems Division provides NIST's administrative computing support.

As a result of rapid advances in computing and telecommunications technology and NIST's increasing demands for high-performance computing and telecommunications, CAML's divisions for providing NIST's central computing and telecommunications services have been particularly proactive in the past several years.

NIST's central computing and telecommunications resources have been improved substantially over the past several years. Although the details of the improvements are not listed here, they are impressive. NIST' s current individual workstation resources are generally satisfactory but must continue to be upgraded from time to time to maintain state-of-the-art computing resources for the staff; e.g., many of the UNIX workstations (Sun stations) currently being used are several years old, especially at the Boulder site, and are being made practically obsolete by the rapid evolution of processors. Also, the silicon graphics systems need additional administrative services.

The current upgrade of Cray and peripheral facilities is needed and well conceived. The panel endorses CAML's proposed file migration testbed to help in selecting cost-effective, strong central computational resources and in evolving increased central support for NIST's local workstations and servers.

Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
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Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
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Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
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Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
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Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 242
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 243
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 244
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 245
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 246
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 247
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 248
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 249
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 250
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
Page 251
Suggested Citation:"11 COMPUTING AND APPLIED MATHEMATICS LABORATORY." National Research Council. 1994. An Assessment of the National Institute of Standards and Technology Programs: Fiscal Year 1993. Washington, DC: The National Academies Press. doi: 10.17226/9192.
×
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