Fourteenth Industrial Mathematical and Statistical Modeling Workshop for graduate students

Fourteenth

Industrial Mathematical and Statistical Modeling

Workshop for Graduate Students

July 21-29, 2008

North Carolina State University

Raleigh, NC

Faculty and postdoctoral mentors

H. T. Banks

1

, Ariel Cintron-Arias

1

, Mansoor Haider

2

, Ilse Ipsen

2

, Grace Kepler

1

,

Mette Olufsen

2

, Tao Pang

2

, Jeff Scroggs

2

, Nell Sedransk

3

, Gentry White

4

, Jasmine

Zhou

3

1. CRSC/CQSB, North Carolina State University, Raleigh, NC 27695-8205

2. Dept of Mathematics, North Carolina State University, Raleigh, NC 27695-8205

3. National Institute of Statistical Sciences, 19 TW Alexander Drive, Durham, NC 27709

4. Dept of Statistics, North Carolina State University, Raleigh, NC 27695-8203

Participants

Sydney

Akapame

Montana State University

Daniel

Beavers

Baylor University

Abhishek

Bhattacharya University of Arizona

Jacob

Blanton

Louisiana State University

Daniel

Cargill

NJ Inst. Of Tech

Matthew

Causley

NJ Inst. Of Tech

Juanjuan

Chai

Indiana University

Nancy

Chalmers

University of South Carolina

Wei

Chen

John Hopkins University

Jintao

Cui

Louisiana State University

Caitlin

Daley

NCSU

Giulio

Genovese

Dartmouth College

Nicholas

Gewecke

University of Tennessee

Marian

Hofer

University of California

Kathleen

Holm

NCSU

Jobby

Jacob

Clemson University

Adarsh

Joshi

Texas A&M University

Yogesh

Joshi

NJ Inst. Of Tech

Manmeet

Kaur

NJ Inst. Of Tech

Viviane

Klein

Oregon State University

Denka

Markova

Baylor University

Linda

Njoh

Baylor University

Lu Ee

Peh

University of Dayton

Peng

Qi

University of Wisconson-Madison

Yu

Qiu

Iowa State University

Lucinda

Robledo

University of California

Shashi

Singh

University of Hawaii

Svetlana

Solovieva

Moscow State University

Jeff

Stanley

Texas A&M University

Shuguang Tan

University of Florida

Solmaz

Torabi

University of California, Irvine

Mark

Walters

University of South Carolina

Nathan

Wanner

NCSU

Justin

Wright

Bloomsburg Univ

Bokai

Yan

University of Wisconson-Madison

Preface

This volume contains the proceedings of the

Industrial Mathematical and Statistical

Modeling Workshop

for graduate students, held at the Center for Research in

Scientific Computation at North Carolina State University (NCSU) in Raleigh, North

Carolina from July 21-29, 2008. This was the fourteenth such workshop to be held at

NCSU, and brought together 36 graduate students from 24 universities.

On the morning of the first day, industrial scientists presented five research problems.

Students were divided into five teams to work on mathematical and statistical modeling

problems presented. In contrast to neat, well-posed academic exercises that are

typically found in coursework or textbooks, the workshop problems are challenging

real-world problems that required the varied expertise and fresh insights of the group for

their formulation, solution and interpretation. Each group spent the first eight days of the

workshop investigating their project and reported their findings in half-hour public

seminars on the final day of the workshop.

This year’s projects were

Cardiovascular events associated with oral and IV-administered antibacterial

agents

Glaxo SmithKline

Presenter: Jeffrey D. Wetherington

Faculty Mentors: Grace M Kepler, HT Banks, and Ariel Cintron-Arias

Estimating position and velocity of flight vehicles using angle-only

measurements

MIT Lincoln Laboratory

Presenter: John Peach

Faculty Mentors: Mansoor Haider, Gentry White

Quantifying normal variation in ECGs

National Institute of Statistical Sciences

Presenter: Nell Sedransk

Faculty Mentors: Mette Olufsen, Nell Sedransk, and Jasmine Zhou

Behavior of dynamic aggregate loss distributions emerging from mortgage

insurance risk

Republic Mortgage Insurance Company

Presenter: Frank Meyer

Faculty Mentors: Tao Pang, Jeff Scroggs

Permuting large entries of a sparse square matrix to its diagonal

SAS Institute

These problems represent a broad spectrum of mathematical and statistical topics and

applications. While the problems included many aspects that are challenging to address

in the nine-day duration of the workshop, readers of this report will observe remarkable

progress on all the projects.

We strongly believe that this type of modeling workshop provides a highly valuable

research related experience for graduate students that simultaneously contributes to the

research of the industrial participants. One of the biggest challenges in real-world

research is defining the problem and identifying what can be done about it. Our

workshop participants get experience in this crucial life skill. In addition, the workshop

improves graduate students’ ability to communicate and interact with scientists who are

not traditional mathematicians, but who require and employ mathematical tools in their

work. Through this unique experience that exposes students to the means by which

mathematics is applied outside academia, the workshop has helped many students

clarify their career aspirations. In several cases, after past workshops, students have

been hired by the participating companies. Students interested in academic careers

also find a renewed sense of excitement about applied mathematics and statistics from

broadening their horizon beyond that which is typically presented in mathematics

graduate education.

Active participation of all involved during a nine day period of almost uninterrupted work,

plus a series of social activities, enhanced the success of the workshop. The organizers

are grateful to the participants for their dedicated effort and contributions.

Funding for the workshop was provided by the Statistical and Applied Mathematical

Sciences Institute (SAMSI) with additional financial support, personnel, and facilities

provided by the Center for Research in Scientific Computation (CRSC) and the

Department of Mathematics at North Carolina State University.

Finally, we would like to express our sincere gratitude to Deborah Leistikow, Lesa

Denning and Mara Gonzalez for their efforts and help in all administrative matters. We

are also grateful to Hien Tran for conducting the CRSC lab demonstration.

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0

0.5

1

1.5

2

−30

−20

−10

0

10

20

30

time (min)

Sensitivity function

Sensitivity of C

P

(t) to Parameters

Q

T

V

M

D

T

0

1

2

3

−20

−15

−10

−5

0

5

10

time (min)

Sensitivity function

Sensitivity of C

A’

(t) to Parameters

Q

T

V

L

T

0

1

2

3

−5

0

5

10

15

time (min)

Sensitivity function

Sensitivity of C

L

(t) to Parameters

Q

T

V

L

E

L

V

0

K

M

T

0

2

4

6

−5

0

5

10

15

20

time (min)

Sensitivity function

Sensitivity of C

H

(t) to Parameters

œRZ?4C ) ; -?.nn1;CFX`4`C%KLG[E‚KIWA1DC ' %'& ))[ W•PRGI4`5•E‚KIWA†D4`5YHJPV4CFPVWAKLWY†;49KI1 ( ECF3 #&%¦œRZ?4C ); -?. _Z?48X1DCFX4CDKIGIEKLWY1;C ' ( ))[ W•PbGI4`5•E‚KIWA†D4`5YH‰PL4`CFPLW‡KIWA†D4 KI1 #&%. ( A §E;CF3 @ 1;CF5AH2E‚KKLWY@B4 ) % ý M›/.b_ZF4¨GI4`5•E‚KLWY†;4 PL4`C)PVWAKLWY†qW‡KIWA4Pb1;Š:' *))[ X[ZFEC?OD4 1‚†;4G KLWY@45?–4`WYC?O‘@B1DPVKGI4`5•E‚KIWA†D4`5YHJPV4CFPLW‡KIWA†D4KI1 uZ?WYO;Z?4PˆKUGI4`5•E‚KIWA†D49PL4`C)PVWAKLWY†qW‡KˆH#)?KLZ?4C # ECF3‰™ .

0

2

4

6

8

10

−50

0

50

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_P

(t) to Parameters

Q

_T

V

_M

D

T

0

2

4

6

8

10

−40

−30

−20

−10

0

10

20

30

40

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_A’

(t) to Parameters

Q

_T

V

_L

T

0

1

2

3

4

−100

−50

0

50

100

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_L

(t) to Parameters

Q

_T

V

_L

E

_L

V

₀

K

_M

T

0

2

4

6

8

10

−2

−1

0

1

2

3

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_H

(t) to Parameters

E

L

Q

_H

V

_H

k

T

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0

0.5

1

1.5

2

−20

−15

−10

−5

0

5

time (min)

Sensitivity function

Sensitivity of C

_P

(t) to Parameters

D

T

0

1

2

3

4

5

−15

−10

−5

0

5

time (min)

Sensitivity function

Sensitivity of C

_A’

(t) to Parameters

D

T

0

2

4

6

8

10

−8

−6

−4

−2

0

2

time (min)

Sensitivity function

Sensitivity of C

_L

(t) to Parameters

D

T

0

2

4

6

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

time (min)

Sensitivity function

Sensitivity of C

_H

(t) to Parameters

D

T

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0

2

4

6

8

10

−1.5

−1

−0.5

0

0.5

1

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_P

(t) to Parameters

D

T

0

2

4

6

8

10

−1.5

−1

−0.5

0

0.5

1

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_A

(t) to Parameters

D

T

0

2

4

6

8

10

−40

−20

0

20

40

60

80

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_L

(t) to Parameters

D

T

0

2

4

6

8

10

−15

−10

−5

0

5

time (min)

Rel. Sensitivity function

Relative Sensitivity of C

_H

(t) to Parameters

D

T

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C

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0

2

4

6

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0

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0.1

0.15

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0

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8

10

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0.02

0.04

0.06

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0

0.2

0.4

0.6

0.8

1

1.2

0

50

100

150

200

Time (minutes)

Dose rate (mg/min)

Two different dosing strategies

Constant Rate Strategy

Triangle Rate Strategy

0

0.5

1

1.5

2

2.5

3

0

1

2

3

4

5

6

Time (minutes)

Concentration (mg/L)

Drug extracted into lung for two strategies

Constant dose rate strategy

Triangle dose rate strategy

0

2

4

6

8

10

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (minutes)

Concentration (mg/L)

Drug in the heart for two strategies

Constant dose rate strategy

Triangle dose rate strategy

0

0.5

1

1.5

2

2.5

3

0

2

4

6

8

10

12

Time (minutes)

Concentration (mg/L)

Concentration into lung for two injection times

Injection over 1 minute

Injection over 1 second

0

2

4

6

8

10

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0.2

0.4

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Time (minutes)

Concentration (mg/L)

Concentration in heart for two injection times

Injection over 1 minute

Injection over 1 second

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1

1.2

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2

1

2

3

4

5

6

7

8

Injection time

Peak lung / peak heart concentration

Effectiveness of two dosing strategies vs. injection time

Constant dose rate strategy

Triangle dose rate strategy

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