ResearchHighlights2012

D e p a r t m e n t o f M a t h e m a t i c s

Table of contents

04 RFID tags and privacy Clliff ord Bergman 06 Generalizations of Apollonian circle packing Steve Butler

08 Developing mission assurance with performance impact analysis in a semi-automated framework Jennifer Davidson

10 Sounds of a boundary value problem: Elliptic partial diff erential equations Gary Lieberman

12 What is relevance? Roger Maddux

14 Position, momentum and research experiences for undergraduates Justin Peters

16 Research in quantum information science Yiu Tung Poon

18 The challenge of complexity Jonathan D.H. Smith

20 The data deluge Eric Weber

22 Published research 2010 through February 2012

30 Department faculty Research areasIowa State University does not discriminate on

the basis of race, color, age, religion, national origin, sexual orientation, gender identity, sex, marital status, disability, or status as a U.S. veteran. Inquiries can be directed to the Director of Equal Opportunity and Diversity, 3210 Beardshear Hall, (515) 294-7612.

Cover fractal created by Dan Ashlock.

linear algebra enable quantum information and quantum computing; algebra enables new approaches to biological structures, etc. It is, indeed, one of the fascinating aspects of mathematical research that very abstract structures and results sometimes, in very unexpected ways, are at the core of new scientifi c and engineering developments.

It is crucial for the Department that we continue to develop timely research in ‘applied’ as well as in ‘theoretical’ areas of mathematics since these areas depend on each other for cross-fertilization and inspiration. Our hiring policies over the last years refl ect the goal of maintaining a balanced approach to core mathematical research, and to interaction with scientists and engineers working on innovations.

If you enjoyed reading the articles found here, or if you have comments or remarks, we would like to hear from you. You may email me at kliemann@iastate.edu, or send mail to the Department of Mathematics, 396 Carver Hall, Iowa State University, Ames, IA 50011.

Wolfgang KliemannProfessor and Chair

The Department of Mathematics at Iowa State University is proud to present its second research publication, Research Highlights 2012.

On the next pages, nine faculty members give short overviews of their research activities. As before, we have tried to strike a balance between more ‘applied’ areas of mathematics, and more ‘theoretical’ ones.

Sometimes mathematical research results do capture the imagination of many people. Examples of this are certainly the solution of Fermat’s last theorem, announced by Andrew Wiles in 1993, and the solution to the graph coloring problem, solved in 1976 by Kenneth Appel and Wolfgang Haken. By the way, we have faculty experts in both number theory (Ling Long) and graph theory (Ryan Martin) at Iowa State – their research was presented in Research Highlights 2010.

It is more common, however, that mathematics contributes to important discoveries and economic developments as part of a research chain, i.e. one link interconnected with work in other fi elds to produce innovations. In such a chain mathematics often plays the role as the language and structure of

modeling, and as the large toolbox of approaches that allow for detailed analysis of the models. While the fi nal discovery or technological innovation may not have mathematics written all over it, quantitative and structural mathematical reasoning and modeling almost always is a key piece of it.

Research Highlights 2010 reported on some research efforts in our department that are part of such an innovation chain, such as cancer research, tissue transfer, or electric power systems. Research Highlights 2012 continues this tradition by discussing faculty contributions to areas such as RFID tags, mission assurance, quantum information science, and mathematical biology. These studies involve many different areas of mathematics, such as algebra, computational mathematics, linear algebra, differential equations, probability, or functional analysis.

Some of these mathematical areas are traditionally considered to be more ‘theoretical’ or ‘pure’ mathematics, but now they are center pieces of some crucial applications of mathematics: algebra and number theory provide the foundation of information security; functional analysis and

3

An RFID tag is an integrated circuit, often about twice the size of a grain of rice. It generally has a small amount of memory holding fi xed data. High-end tags have some modest processing power as well. An RFID tag has no power source of its own. It is dormant, until it comes into close proximity to a reader. The tag obtains its power from the radio waves broadcast by the reader and all communications between the reader and the tag take place on the RF spectrum.

These tags can make for very convenient interactions. An authorized worker can simply wave his or her wallet in front of the reader in order to enter a secure building. If the reader is powerful enough, perhaps the worker will not even have to take the wallet out of his pocket. Similarly, the I-Pass system allows drivers on the Illinois Tollway to pay tolls without actually stopping at the tollbooths. The system simply reads the RFID tag attached to the car windshield and debits the driver’s account.

But there is a dark side to this technology. Just as the reader at the front entrance can identify a worker from his RFID card, anyone possessing a portable reader can do the same. Imagine an employee attends a worker’s-rights meeting. An undercover spy could use a hidden reader to identify all of the employees present. Or consider the tollbooth application. Hidden readers could be used to track an automobile’s location without the driver’s knowledge. Privacy advocates have raised valid concerns about the ubiquitous use of RFID tags.

The characteristics of RFID tags make it diffi cult to implement traditional security measures. For one thing, since the tags have no power source and limited memory, it is impossible for a tag to interrogate a reader or even remember past “conversations” with a given reader. What we seek is a way for this limited-ability tag to determine which readers to trust with its information.

In cryptography and information theory, trust between two entities

is usually established by having the entities share something. Most often, that something is a shared secret, such as a password. In the access control example discussed earlier, a shared secret is probably possible. Since the employee only has to access a limited number of doors, the employee’s ID card could share a secret with each of the doors. But this is probably not possible in the tollbooth scenario, given the large number of drivers and tollbooths.

One potential consumer convenience we have been hearing a lot about recently is the “smart refrigerator”. The idea is that each product purchased would contain an RFID tag, and the refrigerator itself would contain a reader. The refrigerator could maintain an inventory of its own contents and warn the owner when it is time to buy milk. A similar idea is a smart library that tracks the books on its own shelves.

But imagine riding the bus home from the market or bookstore with your new purchases. Anyone with

RFID tags and privacyCliff ord Bergman

Those small plastic gizmos you see attached to many of the things you buy are called RFID (Radio Frequency Identifi cation) tags. They are used for inventory control, product tracking, toll collection, and for controlling access to buildings and offi ces. These tags have advantages over other forms of identifi cation. Unlike bar codes, they can be housed within an object and do not have to be visible. Unlike a key, an RFID tag need not come in physical contact with a lock.

4

a reader could discover what you bought. For books, this is an obvious privacy concern. But even groceries pose privacy issues. In the current political climate in Arizona, walking around with tortillas in your sack might be risky.

In recent research with two Iowa State colleagues, George Amariucai and Yong Guan, I have devised a new technique for addressing this problem. It is particularly suitable for the grocery example. (Not so useful for tollbooths.) Instead of sharing a secret password, the tag and the reader share “quality time” together. That is, when the tag fi rst encounters the reader, it does not trust the reader enough to identify itself. At regular time intervals, the tag gives the reader a small amount of information. It is only if the tag and the reader remain in proximity for a long, uninterrupted, period of time that the reader accumulates enough information to convince the tag that it is trusted. Once the tag trusts the reader, it identifi es itself.

Notice how nicely this solves the refrigerator problem. Right after a shopping trip, your ‘frig won’t know what you bought, but by the next morning it will happily tell you that there is turkey and mayonnaise to pack for today’s lunch. However, the colleague in the next cubicle will not be able to use her reader to decide whether to steal your sandwich.

Both technical and mathematical issues remain to be addressed in our scheme. As I mentioned earlier, RFID tags have very limited computing capabilities. With today’s technology, a tag can contain about 2000 transistors. The algorithm we propose pushes that limit, and probably exceeds it a bit. But there are other algorithms out there that

might operate with fewer gates. Furthermore, until we implement our scheme on actual RFID tags, it won’t be known how workable it is. Our team has a grant proposal pending with the National Science Foundation for funding to do the investigation and carry out the experiments.

On the mathematical side, consider the following scenario. Suppose you carry the same book on the commuter bus each day. An eavesdropper with a reader will not acquire enough information in a single trip to identify the book. But if that same adversary rides the

same bus with you each day, he accumulates several noncontiguous chunks of authentication information. Is it computationally feasible to use these chunks to reconstruct the entire authentication string? We believe the answer is no. In fact, we hope to prove that this problem is “NP-complete.” If we can prove this, I believe we have a potentially marketable system.

Now, what can we do about the tollbooth problem?...

Who else knows how many eggs Cliff has in his refrigerator?

Reference: An automatic, time-based, secure pairing protocol for passive RFID, G. Amariucai, C. Bergman and Y. Guan, Workshop on RFID Security—RFIDSec’11 (Amherst, MA), June 2011.

5

rule repeatedly. A natural question is to determine if other rules for fi lling these holes can also produce packings where all curvatures are integers. There are currently only two other known rules which can do this.

The fi rst rule comes from fi lling in each hole with three circles (see fi gure 1b), this rule is also known as the octahedron packing rule. Gerhard Guettler and Colin Mallows were able to show that the resulting packings had many of the same properties as Apollonian packings, including the possibility of having all integer bends; but with slight differences.

Fact 2: If a, b and c are integers and the curvatures of three mutually tangent circles with ab + ac + bc twice a square number, then every circle drawn in the octahedron gasket will have integer curvature.

An example of such a gasket with all integer curvatures is shown in fi gure 2b. Curiously a kernel of this idea appears on a sangaku (mathematical tablet containing a problem to be worked and pondered) hung in 1821 inside a Japanese temple in Tokyo by Adachi Mitsuaki.

The second rule comes from fi lling in each hole with infi nitely many circles (see fi gure 1c).

This has been dubbed the hexagonal

packing (due to the similarity of hexagons formed when packing pennies in the plane) and was discovered in 2011 by Steve Butler and Ron Graham.

One of the most famous mathematical images is the Apollonian gasket, formed by starting with three mutually tangent circles and repeatedly fi lling in the “holes" between circles by the addition of a single new circle tangent to all three sides of the hole (see fi gure 1a).

Adding new circles creates new holes and we repeat the procedure for all of the created holes. The name Apollonian comes from the ancient Greek geometer Apollonius (262 BC -190 BC) who showed how to fi nd such a circle.

There are a variety of reasons that the Apollonian gasket is so well known. Certainly it helps that the result is a rather beautiful fi gure, an example of a fractal. There are also interesting number theoretic problems related to the circle packings, related to the curvatures of circles.

Curvature is found by taking one over the radius, so the larger the curvature the smaller the circle. A straight line has curvature 0 and we also allow for negative curvatures.

Rene Descartes (1596 - 1650) made the observation given four circles which are tangent to each other that their curvatures are related

in a simple fashion. Namely if a, b, c

and d are the curvatures then(a + b + c + d)2 = 2(a2 + b2 + c2 + d2).

Solving for d in the above equation by use of the quadratic formula we discover that if a, b and c are integers with ab+ac+bc a square number then d is also an integer. The amazing thing is that not only can we get a few of the curvatures in the Apollonian gasket to be integers, but we can get all of the curvatures to be integers! An example of an Apollonian gasket with integer curvatures is shown in fi gure 2a.

Fact 1: If a, b and c are integers and the curvatures of three mutually tangent circles with ab + ac + bc a square number, then every circle drawn in the Apollonian gasket will have integer curvature.

Once we know that all the curvatures can be integers this raises some natural questions about what we can say about which integers are present and which are not. In the last few years there has been tremendous progress in this regard but there is still a surprising amount that is not known.

The Apollonian packing came from taking a simple rule (fi ll a hole with a single circle) and applying the

Generalizations of Apollonian circle packingSteve Butler

Figure 1a Figure 1b Figure 1c Figure 1d

6

and Q is the golden ratio.Instead of packing circles, we

can also pack spheres. For example starting with four tangent spheres we can fi nd a fi fth sphere to “fi ll the void" between them. This leads to Apollonian sphere packings which can also be constructed in such a way that all curvatures are integers.

The hexagonal packing was discovered by looking at a cross section of this sphere packing.

Last summer Steve Butler and Ron Graham started exploring a generalization of the octahedron packing to spheres. Amazingly this packing of spheres has both the Apollonian gasket and the octahedrongasket as different cross sections. A video showing the transition from

one of these gaskets to the other by rotating through cross sections of the sphere packing is on

YouTube at (http://youtu.be/IRykZHOdfbY).These packings produce

beautiful pictures, but also have a mathematical beauty. The rules used to defi ne packings can be described by how the circles are tangent to one another; and essentially every such set of tangency rules will produce a different packing and there are tools to help understand what can be said about the possible curvatures. In higher dimensions things get much more complicated and there are only two known rules for packing spheres (but more should exist). There is still a lot of interesting work to be done in understanding what happens in packing circles and spheres; what sphere packing rules exist; and understanding the cross sections of various sphere packings.

Figure 2a

Figure 2b

Figure 2c

Figure 2d

Fact 3: If a, b and c are integers and the curvatures of three mutually tangent circles with ab + ac + bc three times a square number, then every circle drawn in the hexagonal packing gasket will have integer curvature.

An example of such a gasket with all integer curvatures is shown in

fi gure 2c.These packings are just a few of

infi nitely many possible rules for fi lling in circles. Other rules also produce amazing pictures and satisfy similar properties where we allow ourselves to work with more exotic sets of numbers. An example of this is the icosahedron packing rule (see fi gure 1d for the rule and also fi gure 2d for a corresponding gasket). It can be shown that it is impossible to have all integer curvatures for such a packing; however, it is possible to have all the curvatures be of the form a+bQ where a and b are integer values

Many systems in today’s complex networks of information and devices depend on a number of factors to accomplish their goals. Examples of such systems include a collection of computing environments connected by internal networks; the networks and systems that the Wall Street stock trading fl oor depend on for trading stocks; industrial control systems or computer systems that monitor and control industrial or infrastructure processes; or any system that has components whose failures result in the failure of part or the whole system. For example, a network of computers that are linked by an internal or local network, where there is a connection to the Internet from the local network, is an example of a system. Threats and vulnerabilities in this system could include a weak password, poor protection of cryptographic keys, unauthorized activities such as malware downloading, and fi rewall mis-confi guration. Systems such as these are called mission-critical systems. As can be expected, the complexities of missions-critical systems are challenging to model. Why do we wish to model them? We can gain useful information about the vulnerabilities, strengths, and risks of these systems, and in

doing so, project counter measures, identify current and future threats, and measure the effects of component failures upon the success of the system if we have a mathematical model in our hands.

Four faculty from three

departments – Mathematics, Electrical and Computer Engineering, and Computer Science – have joined efforts and received a seed grant to research such systems. The grant is provided through the Security and Software Engineering Research Center

Developing mission assurance modeling with performance impact analysis in a semi-automated frameworkJennifer Davidson

n ng

8

(S2ERC), supported by the National Science Foundation and funded by Boeing, one of S2ERC’s industrial partners. The research proposes to develop a semi-automated framework for mission assurance modeling and performance impact analysis. Metrics that assess the impact of attacks, component failures, and performance degradation will provide real-time situation-aware guarantees for mission assurance. The goal will be to link qualitative information with quantitative information in such a way as to facilitate the modeling of the interaction between the two and allow quantitative measures of the system that describe the probability of success of various system goals. Qualitative information includes that which can be described in words, or observable but not measurable data, such as mission goals, general system performance requirements, risk factors, etc. Quantitative information includes data from sensors or other sources, quantities measuring various states of the system, etc. A mathematical theory that has been shown capable of modeling the relationships between quantitative and qualitative characteristics is formal concept analysis (FCA). FCA formalizes the philosophical understanding of a concept as a unit of thought that exists in the human brain and links it to items that exist in reality. FCA was developed by a mathematician named Rudolf Wille in the early 1980s, as a way to represent the relationship aspects of how data is connected, using an area of mathematics called lattice theory. Lattice theory allows a partial order on a set of objects, where two objects can either be related or not. Applied to the real world in a mission-critical system, for example, this allows

two components to have some sort of relation together to the mission’s goal, or not. It turns out this is a key property of the modeling of such systems. Take our local computer network example. The requirement of training personnel for security awareness is not related to fi rewall installation between the local network and the Internet, but security training is related to the education level of users of the local network. These characteristics can be described by using FCA.

The faculty, along with two graduate students, will investigate how to develop an FCA model for mission assurance problems that Boeing has presented, and use relational derivatives that FCA analysis can provide to determine the most critical components of the systems. Metrics will be developed to measure the impact of component failures using probabilistic stochastic models. Since there is also a link between FCA and graph theory, issues of graph spectral sparsifi cation will be studied to allow analysis of different levels of granularity of the system.

Finally, the use of a property called Fano’s inequality will be investigated to develop metrics of measuring the trustworthiness of the system’s states. Bringing together mathematics with engineering and computer science can foster unique solutions to diffi cult problems. The faculty have their sights set on using this seed grant to apply for larger grants at the national level, such as Department of Defense and Homeland Security.

Mission-critical goals such as maintaining up-to-the -minute accurate stock statistics are important to assure functionality of the system found on a stock trading fl oor.

System properties such as fi rewall protection and continuing education are important to the successful functioning of the system in a local network.

9

For many years, I have played clarinet with the Ames Municipal Band and fl ute with Flutes and More (and other instruments with other musical groups). These two instruments have very different sounds, and these sounds can be represented as solutions of boundary value problems. As explained in the next paragraph, a boundary value problem is the combination of differential equations in a region and a boundary condition on the boundary of that region. In the case of clarinet and fl ute, the sounds are determined by the same differential equation but different boundary conditions.

Elliptic partial differential equations provide a mathematical description of a number of physical phenomena, with the solutions of such equations representing such diverse quantities as temperature in a solid body or the height of a fl uid surface inside a tube. In each case, the equation describes how the solution changes from point to point inside some region and it must be supplemented by a boundary condition, which prescribes some information about the solution on the boundary of the region. The boundary condition can be simple and prescribe the value of the solution

Sounds of a boundaryvalue problemGary Lieberman

at each point of the boundary or it can be more complicated and prescribe how the solution changes near a point on the boundary. The combination of a differential equation in a region along with a boundary condition on the boundary of the region is known as a boundary value problem, and the solution of such a problem is the quantity of physical interest.

My research is primarily concerned with studying the qualitative behavior of solutions of such problems. Only in a few very special situations can the solution be explicitly determined so it’s useful to know as much as possible about the solutions. For example, if you model the temperature inside a silo full of grain, then you don’t need to know the exact temperature everywhere in the silo, but you do

need to know if the temperature goes above some threshold (which would cause the grain to burn or even explode).

Some of my research has been to determine simple information like estimating the maximum of the solution (which, in the grain example, means determining if the temperature goes above the danger point) but I am more interested in studying the continuity of such solutions, where the word “continuity” is used in its mathematical sense to mean a measure of how fast the solution changes from point to point. Such information is useful for lots of abstract reasons, but there are direct physical applications as well. If you stick a glass tube with constant cross-section (for example a straw) in a pan of water and if the cross-section of the tube has corners (like a square tube,

Lieberman plays a rosewood fl ute during a performance in the Martha-Ellen Tye Recital Hall on campus. Photo by Megan Eagen.

10

for example), then the behavior of the water inside the tube near the corner exhibits a very striking type of behavior. Paul Concus and Robert Finn [2] showed that there is a number 𝛼 such that, when the interior angle at the corner is greater than 𝛼, then the water rises no higher than a certain height (independent of the angle) but, when the interior is less than 𝛼, then the mathematical solution of the model problem goes to infi nity at the corner. Careful experiments show that, even though the water doesn’t go off to infi nity, the height at the corner jumps as the angle is increased from slightly less than 𝛼 to slightly more than 𝛼. Further work by Jean Taylor [7], Leon Simon [6], and myself shows that the solution is actually very well behaved when the angle at the corner is greater than 𝛼.

A recurring theme in my research is that solutions of

certain boundary value problems are more continuous than prior experience would suggest. Here, the measure of continuity may involve the derivative from calculus, which is a measure of rate of change. (If the solution has a derivative somewhere, then it is continuous, but the solution can be continuous somewhere without having a derivative.) In particular, if the boundary condition prescribes the value of the solution at each point and if the region has re-entrant corners, then the solutions of this boundary value problem generally have derivatives near the corners but NOT at the corners; however, if the boundary condition prescribes how fast the solutions changes in appropriate directions, then I showed [4] that the derivatives exist and are continuous near the corners. At about the same time, Pipher [5] gave a very different proof of the

same result. It may appear that this result is a very special piece of the theory but it actually arises in other contexts. One of the more surprising places is in the study of wave propagation. About a dozen years after [4] appeared, Canic, Keyfi tz, and I [1] used this esoteric bit of elliptic theory to examine the behavior of certain shock waves. Such an application is especially noteworthy because shock waves are a measure of discontinuity of solutions and the elliptic theory is concerned with continuity of solutions.

References

[1] S. Canic, B. L. Keyfi tz, and G. M. Lieberman, A proof of existence of perturbed steady transonic shocks via a free boundary problem, Communications on Pure and Applied Mathematics 53 (2000), 484-511.

[2] P. Concus and R. Finn, On capillary free surfaces in a gravitational eld, Acta Mathematica 132 (1975), 207-223.

[3] G. M. Lieberman, Holder continuity of the gradient at a corner for the capillary problem and related results, Pacic Journal of Mathematics 133 (1988), 115{135.

[4] , Oblique derivative problems in Lipschitz domains. I. Continuous boundary data, Bolletino Unione Matematica Italiana B (7) 1 (1987), 1185-1210.

[5] J. Pipher, Oblique derivative problems for the Laplacian in Lipschitz domains, Revista Matematica. Iberoamericana 3 (1987), 455-472.

[6] L. M. Simon, Regularity of capillary surfaces over domains with corners, Pacic Journal of Mathematics 88 (1980), 363-377.

[7] J. Taylor, Boundary regularity for solutions to various capillarity and free boundary problems, Communications on Partial Dierential Equations 2 (1977), 323-357.

Keeping track of temperature inside full silos is necessary to prevent damage or loss of crops stored inside.

11

Do you think the following statement is true or false? “If the moon is made of green cheese, then 2 + 2 = 4.” In a mathematical proof or in a computer programming language, such a statement would be regarded as true. In mathematics, an implication of the form H --> C (read “if H then C”, or “H entails C”, or “H implies C”) is true if the hypothesis H is false or if the conclusion C is true.

Do you think that every statement can be derived from a contradiction? For example, if the moon is made of green cheese and the moon is not made of green cheese, does it follow that 2+2 4? Again, in a mathematical proof or computer program, every statement follows from a contradiction. A formula expressing this is H ^ ¬H --> C (read this as “if H and not H, then C”).

According to the article in the Stanford Encyclopedia of Philosophy on relevance logic, “Many philosophers, beginning with Hugh MacColl (1908), have claimed that these theses are counterintuitive. . . . Relevance logicians claim that what is unsettling about these so-called paradoxes is that in each of them the antecedent seems irrelevant to the consequent.. . . Relevance logicians have attempted to construct logics that reject theses and arguments that commit

What is relevance?Roger Maddux

‘fallacies of relevance’.”Relevance logics were fi rst

presented purely syntactically in the 1960’s. The formulas, axioms, and rules of inference were explicitly described. Nothing was said about what the formulas actually mean, nor whether they are true or false.

Various attempts to provide semantics (meanings) for relevance logics appeared in the 1970’s. The most famous and successful of these attempts was the semantical theory due to Richard Routley and Robert K. Meyer, which is based on a ternary “accessibility” relation. However, as noted in the Stanford Encyclopedia of Philosophy, “the ternary accessibility relation needs a philosophical interpretation in order to give relevant implication a real meaning on this semantics.” Several interpretations have been proposed, but there is still no consensus. In fact, the Routley-Meyer semantics has been charged with being “merely formal, exhibiting no connection with the intended meanings of the logical constants”, and “. . . it is completely obscure what meaning is given to negation in the Routley-Meyer theory. . . ”.

Back in the 1970s I noticed that the Routley-Meyer ternary accessibility relation bears a striking resemblance to the ternary relation used to describe the structure of a relation algebra. At

the time I was studying relation algebras at Berkeley for my dissertation with Alfred Tarski. As Anil Nerode said in a recent review of Tarski’s biography, “he had examined the hundreds of theorems on the algebra of binary relations in Schröder’s algebra of logic and derived them all from a few axioms which he took to defi ne relation algebras. This development later led to the development of Tarski’s set theory without variables. This realized a dream of C. S. Peirce and Ernst Schröder to use the binary relation calculus to represent all of mathematics. It also led to relational programming languages.”

Tarski’s set theory without variables was published as a book in 1987, to which I contributed a simplifi ed defi nition of the “translation mapping” for expressing mathematical statements as relation algebraic equations, and, through a purely algebraic theorem, an alternate proof of the book’s main result, called the Translation Mapping Theorem. Around that time I. Németi of the Hungarian Academy of Sciences improved Tarski’s result by translating mathematics into an even weaker algebraic theory than that of relation algebras, and my PhD. student Andy Ylvisaker is currently extending Németi’s methods to an even weaker algebraic theory, thus solving a problem posed by Németi 25 years ago.

After publishing my book Relation Algebras (Elsevier 2006), I took up a detailed study of relevance logic to see what could be made of the connection

12

between Routley-Meyer semantics and relation algebras. I went to Indiana in 2007 during my Faculty Professional Development Assignment to collaborate with one of the “grand old men” of relevance logic, Mike Dunn, who had also noticed the connection with relation algebras about 20 years ago. Together with his student, Kate Bimbó, we wrote one paper on the connection, and a year later I made a surprising (to me) discovery, that one particularly strong system of relevance logic, called RM, can be completely characterized by commutative relation algebras whose elements are transitive

dense binary relations. Both of these papers appeared in the premier venue for such work, the Review of Symbolic Logic. I am currently attempting to show that the primary system of relevance logic, the one called R (which is RM without the “mingle” axiom), can be characterized in a similar way, using the entire class of relation algebras instead of some special ones.

The import of this work will be a clear and explicit explanation of the “accessibility” relation. Considering the objects as relations, we see that three of them are in the Rouley-Meyer accessibility relation if composing

the fi rst two relations contains the third relation. Peirce and Schröder worked on the calculus of relations in the nineteenth century. Relevance logics were developed independently in the twentieth century, for reasons totally unrelated to the calculus of relations. And yet the two subjects are intimately connected. Is this just a pure coincidence, or is there some underlying reason? There is no sign that the founders of relevance logic were trying to

capture properties of binary relations in their axioms, so perhaps it is just a coincidence. Is that really possible?

13

In quantum statistical mechanics

one has particles or observables, and

operators which operate on them.

Mathematically the particles are

vectors in “Hilbert space”, and two

of the operators are the momentum

operator and the position operator.

Now the famous Heisenberg

Uncertainty Principle states that

one cannot know, at a given instant,

both the position and momentum

of a particle, as a measurement of

Position, momentum, and research experiences for undergraduate studentsJustin Peters

either one of the quantities changes

the other. In other words, applying

the position operator fi rst changes

the momentum, or applying the

momentum operator changes the

position of the particle. In other

words, applying the position operator

fi rst and then the momentum

operator does not yield the same

result as applying the momentum

operator fi rst followed by position.

Mathematically, we say that the two

operators do not commute.

I work in operator algebras, a

part of mathematics that grew out of

statistical quantum mechanics. The

history of mathematics is closely

tied to developments in physics,

and over time advances in one fi eld

have infl uenced the other. Today,

the fi eld of operator algebras is an

active fi eld of mathematics, both in

the U.S. and internationally. Over

my career I have worked on various

aspects of questions arising from the

Uncertainty Principle, though this

link to physics is rarely explicit in the

literature.

There is also a large overlap of

operator algebras with dynamical

systems. Some of my work has been

in this area. I currently have research

projects in operator algebras ongoing

with collaborators in North Dakota

State University and the University

of Waterloo, looking at groups and

semigroups of linear operators, their

generalizations and applications.

One mode of research that has

become quite popular is doing

research with undergraduate

students. Leslie Hogben and I have

a grant from the National Science

Foundation which supports research

experiences for undergraduates

(REU) in mathematics at Iowa State

during the summer. For most of

my career, research in mathematics

with undergraduates was relegated

to second tier institutions, as

many believed that only by going

through years of graduate study

could students be in a position to

contribute to mathematical research.

One of the remarkable changes that

has taken place over the past decade

is that it is now recognized nationally

Peters uses this image to illustrate the famous Heisenberg Uncertainty Principle, which states that one cannot know, at a given instant, both the position and momentum of a particle.

14

that outstanding undergraduates

are indeed capable of undertaking

research in mathematics, with careful

mentoring. For me, this has been

an exciting development, and I’m

glad that we at Iowa State have been

part of it. We now have our second

REU grant, and many faculty in the

department have participated as

mentors.

In 2009 I proposed an REU project

in symmetric norms on Euclidean

space. A norm is one of the basic

tools of analysis; it can be thought of

as a way of measuring distance. The

group of four students, who came

from all over the country (Brown

University, Berkeley, University of

Pittsburgh, and the University of

Puerto Rico) did some very nice work

on this topic. That work has led to

an ongoing research seminar which

is attempting to extend some of these

results.

Another REU project, which

ran in summer of 2011, was

devoted to matrices of continuous

functions. Two of the basic courses

of the undergraduate mathematics

curriculum, linear algebra and

introductory analysis (which centers

around the study of continuous

functions) come together in this

project. The group discovered

an algorithm to solve a basic

problem—how to diagonalize a

matrix of continuous functions—

that, surprisingly, had not been

done before. The group also did an

analogue of the Cayley-Hamilton

theorem for such matrices. The

graduate student who helped mentor

the REU students last summer is

working with me to edit the paper

the students wrote, preparing it for

submission to a research journal.

Another of my research related

activities has been in working with

students in Peru. There I have

been presenting research results to

students at the Universidad Nacional

San Agustin de Arequipa, in Peru,

where I have been invited to lecture

during the past fi ve years. This work

with Peruvian students is symbiotic

with the REU projects; each gives

me ideas for the other. There is a

great need to develop scientifi c and

mathematical competency in Peru,

and I have found the work very

satisfying. As appreciation for my

efforts, I was named to an honorary

faculty position at the university in

May, 2010.

While looking at symmetric norms during the fi rst REU project, students considered ways to illustrate the symmetry.

Can you identify the symmetries of this image?

Peters in Arequipa, Peru with undergraduate students who attended his series of lectures on symmetric norms.

15

This is the age of information. One measure of the rapid advance in information technology is in the changes in storage devices. As the size of the device decreases (from 8.5” and 5.25” fl oppy disks to 3.5” disks, to fl ash memory), its capacity has increased dramatically (from 80 kB to 32 GB = 32,000,000 kB). Similar advances have occurred inside the computer. The number of transistors on an integrated circuit doubles every two years, a trend known as Moore’s law. How far can such miniaturization go? Ironically, as a result of the exponential rate of advance in the last few decades, the end is near. As the manufacturing process gets down to the nanoscale, the quantum effect kicks in. Quantum mechanics is one of the two major advances in Physics in the twentieth century. It was noticed that at atomic scale, things behaved very differently from what classical physics had predicted. Ever since its discovery, quantum mechanics has been applied with enormous success to everything under and inside the Sun, including the structure of atoms, nuclear fusion in stars, superconductors, the structure of DNA, and the elementary particles of nature.

Digital computers used today are built on the principle of classical physics. Richard Feynman (Nobel Laureate in Physics, 1965) had realized that there seemed to be essential diffi culties in simulating quantum mechanical systems on such

computers. In 1981, he suggested that building a computer that uses the effects of quantum mechanics would allow us to avoid those diffi culties. For some time, Feynman’s idea was only of theoretical interest, but scientifi c developments on the subject in the last few decades have brought the idea to the attention of researchers from different areas, and stimulated much research activities*. This leads to the new area of research in quantum information science.

Quantum information science is a rapidly growing research area. The study concerns the use of quantum effects in constructing fast computing devices (quantum computers) and designing secure communicating schemes. Quantum algorithms running on these new computers can solve problems much more effi ciently than digital computers. For example, most security protocols used in digital information communication today are based on the assumption that it takes a long time to factor a large integer on current digital computers. However, in 1994, Peter Shor formulated a quantum algorithm which can factor an integer much faster on a quantum computer. Using this algorithm on a quantum computer, one can decrypt the commonly used RSA public key cryptography system more effi ciently. This will have a signifi cant impact on security issues

in communications and commercial activities. On the other hand, one can use the quantum effects such as superposition and entanglement to construct secure communication schemes, which help distribute public key and improve cryptography systems. In fact, a quantum cryptography scheme has already been used in fi nancial transactions and elections. However, some issues in technological applications remain to be settled.

One major challenge in information science is that during the transmission, storage or operation on information, noises can occur. For example, classical information uses the binary system. Information is represented by a sequence of 0’s and 1’s. Noises in the environment can fl ip a 0 to 1 or vice versa. An effective tool to combat noises is using error correcting codes. A message of (0,1) sequence is encoded into a longer (0,1) sequence. Suppose during transmission, some of the 0’s and 1’s are fl ipped. When the sequence is received, one would apply decoding to recover the original sequence. The process is like wrapping a glass with paper before moving. During transportation, the wrapping paper may get crumpled. However, if we wrap the glass with care and no major accidents occur, we can expect the glass to remain intact when we

Research in quantum informationscienceYiu Tung Poon

Poon illustrates that in the case of storage devices over the years, less is more--from the early 8.5” fl oppy to today’s fl ash drive.

80 kB 140 kB 1 MB 100 MB 32 GB

16

unwrap it at the destination. One can apply similar principles

to error correcting codes in quantum information. However, there are some important differences between classical information and quantum information. The basic unit for classical information is a bit which can be in one of two states (0 or 1). The basic unit of quantum information is a qubit which can be in an infi nite number of states. Furthermore, we have to deal with the following diffi culties in the handling of quantum information:

(1) Classical information can be easily duplicated. This can be used in the 3-bit encoding scheme as follows. Suppose we have a bit of information represented by x, then we can use 3 copies of x, i.e. xxx, as the encoded message. If at most one error occurs during transmission, then the received message has one of the following forms: xxx, yxx, xyx, xxy. Therefore, the original information can be recovered using the majority rule. However, according to the No-cloning Theorem, we cannot build a device that can duplicate any unknown qubit.

(2) Error for a bit of classical information is simple. It fl ips a 0

to 1 or 1 to 0. However, an infi nite number of different errors can occur to a single qubit.

(3) In classical information, when an encoded message is received, we can observe the whole sequence of 0’s and 1’s to fi nd out what errors might have occurred before applying the decoding procedure. In quantum information, only partial information of a quantum state can be obtained by observation and the state is usually collapsed in the observation process.

For the above reasons, error

correction in quantum information is much more complicated and the mathematical tools required are more sophisticated than those used in classical information.

A key result in quantum error correction is the Knill-Lafl amme Theorem which gives a necessary and suffi cient condition for the existence of an encoding-decoding scheme to correct a given error pattern. The condition can be described by a mathematical object known as the higher rank numerical range. The study of (classical) numerical range began with the work of Toeplitz and Hausdorff 100 years ago. Since then, many generalized numerical ranges

have been studied and important applications to different branches of mathematics have been established. Higher rank numerical range is the most recent generalization in connection with quantum error correction. Poon’s research on generalized numerical ranges began more than 30 years ago when he studied for his master degree at the University of Hong Kong. He is excited to fi nd its recent application to the study of quantum error correction.

Quantum information science research is inherently multi-disciplinary, as it draws signifi cantly on aspects of mathematics, physics, computer science, information theory, engineering and chemistry. Recently, Poon’s research on the subject has led to collaboration with scientists in China, Germany, Japan and the U.S. Since 2008, he has 12 papers published in the area. One of his papers in 2009 was selected a most cited paper. His research work is supported by an NSF grant in the U.S. and an RGC grant in Hong Kong.

Information becomes encoded before it is transmitted; the message is then decoded upon delivery.

* For the recent IBM news release, see www-03.ibm.com/press/us/en/

pressrelease/36901.wss

17

Mathematics is the central discipline of science, so sciences advance and mature by becoming mathematical. Physics was the fi rst science to reach this stage of maturity, with particular impetus starting in the middle of the second millennium. A great deal of modern mathematics has emerged, and continues to emerge, from the interplay between mathematics and physics, while many present-day mathematical models and ways of thinking are based on prototypes from physics. The models are characterized by reference to a single, pervasive, underlying space-time, based on the dynamics of billiard balls, planets, or photons. The ways of thinking are reductionist, aiming to explain high-level phenomena in terms of “fundamental” low-level activity.

We are now witnessing the start of a major revolution in mathematics, as sciences once considered beyond its range, such as biology and social sciences, are beginning to become mathematical. For the moment, most of the mathematics that appears in these disciplines is devoted to the

treatment of limited subsystems that are modeled as if they were part of physics. But the real challenge is to develop mathematical techniques for handling complex systems that operate on multiple levels, where the parameters at the different levels do not bear any linear relationship to each other. Much of my work is concerned with this challenge.

Time parameters in biology provide a direct example of complexity. Certainly, biological processes unfold against the background of physical time, so-called calendar time. However, for an individual organism, its life history is governed by an internal, logarithmic

time. Consider a typical human lifespan of 80 years. Measured by logarithmic time, the intervals from 5 to 10 years old, from 10 to 20 years old, from 20 to 40 years old, and from 40 to 80 years old, are all equal. This matches with human experience, where the “teenage” memories from 10 to 20 years old are roughly equal to the memories from 20 to 40 years old. Since there is no constant scaling between universal calendar time and the logarithmic time of an organism’s life history, the internal functioning of the organism takes place on a different level from the level of regular physical processes.

Paradoxically, modeling real-world phenomena as complex systems may lead to a simpler, more powerful analysis than that provided by classical techniques. Human demography provides a

good example. Traditionally, the local demographics of a country were modeled by dividing the female population into 5-year age classes, studying the survival rates from each class to the next, and the average number of female babies born to a woman as she sojourned in each of the age classes (Fig. 1). An instantaneous snapshot of the population required lots of individual entries in a so-called Leslie matrix, one entry for each of the arrows in the fi gure. If the population is modeled as a complex system, with one level operating on calendar time, and the other on a mother’s internal logarithmic time, then the entire instantaneous description can be reduced to a single vector of fi ve parameters. What is more, this

vector may then be tracked over time to give a realistic, dynamic view of the evolution of the population. (By contrast, there is no good way to relate the Leslie matrix entries over successive time periods as the constitution of the population changes.) For an example of the power of the new approach, consider the graph in Fig. 2, showing the number of babies born to mothers of various age classes in peninsular Malaysia according to the 1985

The challenge of complexityJonathan D. H. Smith

Fig. 1: Five-year age classes.

18

Fig. 3: Competition between an unstructured and a structured species.

fi gures. The solid line traces the exact numbers, while the dotted line traces the births predicted by the complex systems model based on tracking its fi ve-parameter vector from the 1970, 1975, and 1980 data. The prediction is remarkably close to the actual observations.

New mathematical tools are being developed to analyze complex systems that operate on multiple levels. One thrust of my research is focused on barycentric algebras, which embody convex sets at each of an ordered set of levels. Convex sets are sets in space with a special property: Whenever they contain two points, they contain the entire line segment joining those two points. While classical optimization techniques are based on a single convex set, optimization in barycentric algebras may embrace all the levels of a complex system. As an elementary

example, consider the competition between an unstructured species and a species with two stages (Fig. 3). The internal distribution of the two stages of the stage-structured species takes place at the demographic level, while the competition between the two species takes place at the ecological level. A single barycentric algebra is able to analyze the entire complex system. One of the most interesting ideas to emerge from such an analysis is the concept of a virtual species, a coherently functioning combination of individuals from different species. The virtual species concept enables one to give an explanation for the evolutionary success of domesticated species: While they might have no basis for success on their own, they are coupled to humans in a very successful virtual species.

Another aspect of my research is

concerned with symmetry in complex systems, which most often takes the form of an approximate symmetry, such as the bilateral symmetry of mammals. While exact symmetries are described algebraically by groups, approximate symmetries may appear algebraically as quasigroups. A major program, spanning many decades, has been devoted to extending various aspects of group theory to the broader context of quasigroups. While groups, such as integers under addition, satisfy the associative law x+(y+z)=(x+y)+z, quasigroups are not necessarily required to be associative. Integers under subtraction provide the most direct instance of this phenomenon. For example, 5-(3-2)=4, while (5-3)-2=0. The non-associative subtraction of integers is actually more fundamental than addition, since every integer can be created from 1 by repeated subtractions (suitably bracketed), while repeated additions of ones can only create positive integers.

Fig. 4: Approximate bilateral symmetry

Fig. 2: Births by age class of mother, Malaysia 1985.

19

The data delugeEric Weber

“The Data Deluge” was a headline of a magazine article in The Economist from February 2010. However, this has been a topic of discussion amongst mathematicians for more than a decade. The Data Deluge refers to the fact that modern science, and even modern business, is now driven by immense amounts of information. This information comes from scientifi c measurements, images, web searches, and much more. We have an abundance of data—more data than we know how to handle. Ironically, despite the fact that we have so much data, often it is not enough!

An example of this seeming paradox is what is now known as the Netfl ix problem. Netfl ix users have the opportunity to rate movies that they watch. Netfl ix wishes to take these ratings to predict what other movies those users might enjoy, and then recommend them to the users. Netfl ix in fact instituted a competition with up to a $1,000,000 prize for a team that could design a way to do this. The data that the contestants had at their disposal was 100,000,000 ratings by 400,000 users of over 17,000 movies. One attempt to solve the Netfl ix problem is to form a matrix where each user corresponds to a row, and each movie corresponds to a column, and entry of this matrix in column

A and row B is the (numerical) rating that user B gave (or would give) to movie A. This is a matrix involving 6.8 billion entries, of which we only know 100 million! The Netfl ix problem then becomes trying to estimate the missing 6.7 billion entries. A solution to this matrix completion problem is to fi ll in the missing entries in such a way that the complete matrix has the smallest rank possible.

A more serious example of this type of problem arises in medical

imaging. A CAT scan is an image of the interior of a human body reconstructed from measurements made in the CAT machine. In this case, the reconstruction essentially requires an infi nite number of measurements, but we only have fi nitely many to use! How can this be? We know additional information about the image that we are attempting to reconstruct—the technical description is that the image is bandlimited. This allows us a fairly good

Data arrives from many sources and in many formats.

The * entries represent data that we do not have, but wish to estimate. We make the assumption that the reviewers’ ratings have patterns, for example, by genre, favorite performers, etc. Since there are much fewer of these criteria versus overall movies, we assume that the missing ratings are highly interrelated, which we express mathematically as saying that this matrix has the smallest rank possible. The rank is a measurement of the correlations of the columns of the matrix. A matrix with small rank has high interdependency among its columns.

20

approximation with only fi nitely many measurements.

Much of my research has been in the same vein—how to reconstruct missing information from data which may be incomplete. Information is modeled by a function, and data, or measurements, are values of the function. Thus, the problem becomes determining an unknown function from its values at various points. Currently I am working on two long term projects related to this.

This is a conjecture about the behavior of certain operator algebras (see the article on page 14), but my work has shown that this problem is in fact intimately related to the Heisenberg Uncertainty Principle of quantum physics. In fact, my fi ndings indicate that if this conjecture is true, then there is something of a “Super”-Uncertainty Principle that holds.

In a physics setting, the Uncertainty Principle says that we cannot know with arbitrary precision both the position and the momentum of a subatomic particle. When stated in this way, it says that there is an upper bound on the amount of information we may possess about said particle. However, this can be turned on its head. In a mathematics setting, the Uncertainty Principle says that a function cannot be both spacelimited and bandlimited. In other words, a function cannot be 0 in lots of places in its domain while at the same time its Fourier

transform is also 0 in lots of places in its domain. (The Fourier transform of a function is a way of describing that function in terms of its frequency content.) We can use this to our advantage as follows: if we have an unknown function with the property that its Fourier transform is 0 in lots of places, i.e. bandlimited, then we only need to know the value of the function at a few points, and we can reconstruct all of the rest of its values from the few that we know. This is exactly what makes the CAT scan work.

My results suggest that if the Kadison-Singer conjecture is true, then we can recover an unknown function from even fewer values than we can currently.

The second project concerns polynomials: what if the function we are trying to recover from a few of its samples is a polynomial? Vandermonde’s work in the 17th century shows how this can be done. If a polynomial has degree N, then we can recover all of the values of this polynomial if we know its values at N+1 points. As an example, the following polynomial has degree 3 (the largest exponent): f(x) = x3 + 2x2 + x + 3 and has four terms. If we didn’t know that this is the function f, but we only know that it is a polynomial of degree 3 and we know the values f(1), f(2), f(3), f(4), then we can determine that f is as above.

What if the degree of the polynomial is unknown? I (along with several collaborators) have (re-)discovered that if instead

of knowing the degree of the polynomial what is suffi cient is knowing the number of terms in the polynomial. By combining the work of Vandermonde with an algorithm published by Gaspard de Prony in 1795, a polynomial with N terms (not degree) can be reconstructed from its values at 2N points. For example, suppose the unknown polynomial is xxx g(x) = x101 + 2 x22 + x + 3 which has degree 101 but still only four terms. Vandermonde’s recovery algorithm would require the values of g at 102 points, but now we only need the values of g at 8 points!

Hopefully, these fi ndings can be used in the currently widespread fi eld of Constructive Approximation. For example, the Stone-Weierstrass Theorem says that a continuous function can be approximated by a polynomial. The proof of the theorem says that this is possible, but interestingly it does not say how to fi nd this polynomial. I am working on using this idea of recovering an unknown polynomial of unknown degree to construct the polynomial that necessarily exists by the Stone-Weierstrass Theorem. If successful, this could have wide-ranging impacts, in areas such as medical imaging, weather prediction, and data mining—anywhere there is a “Data Deluge”.

Project 1: The Kadison-Singer Problem

Project 2: Polynomials and functions

21

Research publications 2010-February 2012 Department affi liates in bold

Ackerman, D., J.W. Evans. Boundary conditions for continuum step fl ow models from coarse-graining of discrete 2D deposition-diffusion equations. SIAM Multiscale Modeling & Simulation, 9, 59-88, 2011.

Ackerman, D., J. Wang, J.H. Wendel, D.J. Liu, M. Pruski, J.W. Evans. Catalytic conversion reactions mediated by single-fi le diffusion in linear nanopores: Hydrodynamic versus stochastic behavior. Journal of Chemical Physics, 134, (11) 2011.

Albertini, F., D. D'Alessandro. Dynamics and control theory of quantum walks on graphs. IMA Preprint Series 2324, 2010.

Albertini, F., D. D'Alessandro. Controllability of quantum walks on graphs. To appear in Mathematics of Control Signals and Systems.

Albertson, M., J. Pach, M. Young. Disjoint Homometric Sets in Graphs. ARS Mathematica Contemporanea, 4,1-4, 2011.

Allen, A., S. W. Hansen. Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam. Discrete and Continuous Dynamical Systems, 14 (4), 1279-1292, 2010.

Almodovar, E., L. DeLoss, L. Hogben, K. Hogenson, K. Murphy, T. Peters, C.A. Ramírez. Minimum rank, maximum nullity and zero forcing number for selected graph families. Involve, 3 (4), 371-392, 2010.

Alturk, A., F. Keinert. Regularity of boundary wavelets. Applied and Computational Harmonic Analysis, 32 (1), 65-85, 2011.

Amariucai, G.T., C. Bergman, Y. Guan. An automatic, time-based, secure pairing protocol for passive RFID. Workshop on RFID Security---RFIDSec’11 (Amherst, MA), 2011.

Anderson, D. R., S. Noren, B.Perreault. Young's integral inequality with upper and lower bounds. Electronic Journal of Differential Equations, 74 (10), 1-10, 2011.

Archer, M., M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martinez-Rivera, A. Ochoa. Constructions of potentially eventually positive sign patterns with reducible positive part. To appear in Involve.

Arora, P., W. Li, P. Piecuch, J.W. Evans, M. Albao, M.S. Gordon. Diffusion of atomic oxygen on the Si(100) surface. Journal of Physical Chemistry C, 114 (29), 12649-12658, 2010.

Athreya, K B., J. R. Peters. Continuity of translation operators. Proceedings of the American Mathematical Society, 139 (11), 4027–4040, 2011.

Axenovich, M., J. Choi. On colorings avoiding a rainbow cycle and a fi xed monochromatic subgraph. Electronic Journal of Combinatorics, 17(1), 2010.

Axenovich, M., J. Choi. A note on monotonicity of mixed Ramsey numbers. Discrete Mathematics 311, 2020–2023, 2011.

Axenovich, M., J.P. Hutchinson, M.A. Lastrina. List precoloring extensions in planar graphs. Discrete Mathematics, 311 (12), 1046-1056, 2011.

Axenovich, M., J. Manske, R. Martin. Q2-free families in the Boolean lattice. Order 29 (1), 177–191, 2012.

Axenovich, M., R. Martin. On edit distance in multicolored graphs and directed graphs. To appear Journal of Combinatorics.

Ayala, V., W. Kliemann, F. Vera. Isochronous sets of invariant control systems. Systems & Control Letters 60, 937-942, 2011.

Barioli, F., W. Barrett, S. Fallat, H. T. Hall, L. Hogben, B. Shader, P. van den Driessche, H. van der Holst. Parameters related to tree-width, zero forcing, and maximum nullity of a graph. To appear in Journal of Graph Theory.

Barioli, F., W. Barrett, S. M. Fallat, H. T. Hall, L. Hogben, B. Shader, P. van den Driessche, H. van der Holst. Zero forcing parameters and minimum rank problems. Linear Algebra Applications. 433, 401–411, 2010.

Barioli, F., W. Barrett, S. Fallat, H. T. Hall, L. Hogben, H. van der Holst. On the graph complement conjecture for minimum rank. Linear Algebra Applications, In press.

Basak, T. Finite topological spaces and Poincare duality, Geometriae Dedicata, 147 (1), 357-387, 2010.

Basak, T. On Coxeter diagrams of complex reection groups. To appear in Transactions of the American Mathematical Society. arXiv:0809.2427

Behn, A., I. Correa, I. Hentzel. On fl exible algebras satisfying x(yz) = y(zx). Algebra Colloquium, 17 (1), 881-886, 2010.

Behn, A., K. Driessel, I. Hentzel, K. Vander Velden, J. Wilson. On a tridiagonal nilpotent matrix. To appear in Linear Algebra and Applications.

Behn, A., I. Hentzel. Idempotents in plenary train algebras. Journal of Algebra 324(12), 3241-3248, 2010.

belcastro, s.m., M. Young. 1-factor covers of regular graphs. Discrete Applied Mathematics,159 (5), 281-287, 2011.

Belianinov, A., B. Unal, K.-M. Ho, C.-Z. Wang, J.W. Evans, M.C. Tringides, P.A. Thiel. Nucleation and growth of Ag islands on the (3x3)R30˚ phase of Ag on Si(111). Journal of Physics-Condensed Matter, 23, 265002, 2011.

Ben-Ari, I., K. Boushaba, A. Matzavinos, A. Roitershtein. Stochastic analysis of the motion of DNA nanomechanical bipeds.

22

Bulletin of Mathematical Biology, 73 (8), 1932-1951, 2011.

Ben-Ari, I., A. Matzavinos, A. Roitershtein. On a species survival model. Electronic Communications in Probability, 16, 226-233, 2011.

Bergman, C. Universal Algebra: Fundamentals and Selected Topics, ix+308pp., Taylor & Francis, August 2011.

Berman, A., M. Catral, L. M. DeAlba, A. Elhashash, F. J. Hall, Frank, L. Hogben, I.J. Kim, D. D. Olesky, P. Tarazaga, M. J. Tsatsomeros, P. van den Driessche. Sign patterns that allow eventual positivity. Electronic Journal of Linear Algebra, 19, 108-120, 2010.

Bhattacharyya, G., S.Y. Song, R. Tanaka. Terwilliger algebras of wreath products of one-class association schemes. Journal of Algebraic Combinatorics, 31 (3), 455- 466, 2010.

Bremner, M., I. Hentzel, L. Peresi, M. Tvalavadze, H. Usefi . Enveloping algebras of Malcev algebras. Commentationes Mathematicae Universitatis Carolinae, 51 (2), 157-174, 2010.

Brouwer, A.E., O. Olmez, S. Y. Song. Directed strongly regular graphs from (one-and-half)-designs. European Journal of Combinatorics, 33, 1174-1177, 2012.

Buhler, J., S. Butler, R. Graham, E. Tressler. Hypercube orientations with only two in-degrees. Journal of Combinatorial Theory, Series A 118, 1695-1702, 2011.

Butler, S. Cospectral graphs for both the adjacency and normalized Laplacian Matrices. Linear and Multilinear Algebra 58 , 387-390, 2010.

Butler, S. Eigenvalues of 2-edge-coverings. Linear and Multilinear Algebra, 58, 413-423, 2010.

Butler, S., F. Chung. Small spectral gap in the combinatorial Laplacian implies Hamiltonian. Annals of Combinatorics, 13, 403-412, 2010.

Butler, S., F. Chung, R. Graham, M. Laczkovich. Tiling polygons with lattice triangles. Discrete & Computational Geometry, 44, 896-903, 2010.

Butler, S., K. Costello, R. Graham. Finding patterns avoiding many monochromatic constellations. Experimental Mathematics, 19 (4), 399-411, 2010.

Butler, S., R. Graham, Iterated triangle partitions. Fete of Combinatorics and Computer Science, G. Katona, A. Schrijver, T.Szonyi, eds., Bolyai Society Mathematical Studies 29, Springer-Verlag, Heidelberg , 23-42, 2010.

Butler. S., R. Graham. Enumerating (multiplex) juggling sequences. Annals of Combinatorics, 13, 413-424, 2010.

Butler, S., R. Graham. Shuffl ing with ordered cards. Journal of Combinatorics, 1, 121-139, 2010.

Butler, S., R. Graham, G. Guettler, C. Mallows. Irreducible Apollonian confi gurations and packings. Discrete & Computational Geometry, 44, 487-506, 2010.

Butler, S., R. Graham, J. Mao. How to play the majority game with a liar. Discrete Mathematics, 310 , 622-629, 2010.

Butler, S., J. Grout. A construction of cospectral graphs for the normalized Laplacian. Electronic Journal of Combinatorics, 18 (231), 2011.

Butler, S., P. Horn, E. Tressler. Intersecting domino tilings. The Fibonacci Quarterly, 48, 114-120, 2010.

Butler, S., P. Karasik. A note on nested sums. Journal of Integer Sequences, 13, 2010.

Carlson, B. C. Permutation symmetry for theta functions. Journal of Mathematical Analysis and Applications. www.elsevier.com/locate/jmaa 378, 42-48, 2011.

Catral, M., C. Erickson, L. Hogben, D. D. Olesky, P. van den Driessche. Sign patterns that allow strong eventual nonnegativity. Electronic Journal of Linear Algebra, 23, 1-10, 2012.

Catral, M., L. Hogben, D. D. Olesky, P. van den Driessche. Sign patterns that require or allow power-positivity. Electronic Journal of Linear Algebra, 19, 121-128, 2010.

Chau, H.F., C.K. Li, Y.T. Poon, N. S. Sze. Induced metric and matrix inequalities on unitary matrices. Journal of Physics A: Mathematical and Theoretical, 45 (9), 2012.

Cheng, J., R. Ng. On Hopf algebras of dimension 4p. Journal of Algebra, 328 (1), 399-419, 2011.

Colonius, F., A.J. Homburg, W. Kliemann. Near invariance and local transience for random diffeomorphisms. Journal of Difference Equations and Applications, 16 (2-3), 127-141, 2010.

Cominetti, O., A. Matzavinos, S. Samarasinghe, D. Kulasiri, S. Liu, P.K. Maini, R. Erban. DifFUZZY: A fuzzy clustering algorithm for complex data sets. International Journal of Computational Intelligence in Bioinformatics & Systems Biology, 1(4), 402-417, 2010.

Correa, I., I. Hentzel, A. Labra. Solvability of commutative right-nil algebras satisfying (b(aa))a = b((aa)a). Proyecciones Journal of Mathematics, 29 (1), 9-15, 2010.

Cornette, J. L., R.A. Ackerman. Calculus for the Life Sciences: A Modeling Approach. Volume I, The First Year Course. Self-Published through CreateSpace, Charleston, SC 29418, 2011.

Cornette, J. L., R.A. Ackerman. 2012. Calculus for the Life Sciences: A Modeling Approach. Volume II, Difference and Differential Equations. Self-Published through CreateSpace, Charleston, SC 29418.

23

Cornette, J.L., R.A. Ackerman, B.A. Keller, G.B. Johnston. A “Wet-Lab” Calculus for the Life Sciences. To appear in Ledder, Glen, Carpenter, Jenna P., and Comar, Timothy, Eds., Undergraduate Mathematics for the Life Sciences: Processes, Models, Assessment, and Directions, a volume of the Mathematical Association of America Notes, Washington, D.C.

Csernenszky, A., R. Martin, A. Pluhár. On the complexity of Chooser-Picker positional games. Integers (electronic) 11, 2011, Research Paper G2.

Cummings, J., M. Young. Graphs containing a K3 are 3-uncommon. Journal of Combinatorics, 2, 1-14, 2011.

D'Alessandro, D. Connection between continuous and discrete time quantum walks; From D-dimensional lattices to general graphs. Reports on Mathematical Physics, 66, 85-102, 2010.

D'Alessandro, D. Constructive decomposition of the controllability Lie algebra for Quantum systems. IEEE Transactions on Automatic Control, 1416-1421, June 2010.

D'Alessandro, D., R. Romano. A method for exact simulation of quantum dynamics. Journal of Physics A:Mathematical and Theoretical, 45, (2) 025308, 2012.

D'Alessandro, D., R. Romano. Indirect Controllability of Quantum Systems; A Study of two Interacting Quantum Bits. To appear in IEEE Transactions on Automatic Control, Special Issue on Quantum Control.

Davidson, J., J. Jalan. Steganalysis using Partially Ordered Markov Models. 12th Information Hiding Conference, Calgary, Canada, LNCS, 6387/2010, 118-132, 2010.

Davidson, J., J. Jalan. Canvass - A Steganalysis forensic tool for JPEG images. 2010 ADFSL Conference on Digital Forensics, Security and Law, St. Paul, MN, May 2010.

Davidson, J., J. Jalan. Feature selection for steganalysis using the mahalanobis distance measure. Proceedings of SPIE - The International Society for Optical Engineering, 7541, Media Forensics and Security XII, San Jose, CA, 2010.

DeLoss, L., J. Grout, L. Hogben, T. Mackay, J. Smith, G. Tims. Techniques for determining the minimum rank of a small graph. Linear Algebra and its Applications, 432, 2995–3001, 2010.

Degond, P., H. Liu, D. Savelief, M.H. Vignal. Numerical approximation of the Euler-Poisson- Boltzmann model in the quasineutral limit. Journal of Scientifi c Computing Online First, May 11, 2011.

Doty, D.S., J.H. Lutz, M.J. Patitz, S.M. Summers, D. Woods. Intrinsic universality in self-assembly. Proceedings of the Twenty-Seventhth International Symposium on Theoretical Aspects of Computer Science (STACS 2010, Nancy, France), Schloss Dagstuhl LZI, 275–286, 2010.

Duguet, T., B. Unal, Y. Han, J.W. Evans, J. Ledieu, C.J. Jenks, J.M. Dubois, V. Fournee, P.A. Thiel. Ag thin fi lms on the twofold surface of decagonal Al-Cu-Co quasicrystal. Physical Review B, 82, 224204, 2010.

Duguet, T., Y. Han, C. Yuen, D. Jing, B. Unal, J.W. Evans, P.A. Thiel. Self-assembly of metal nanostructures on binary alloy substrates. Proceedings of the National Academy of Science, 108, 989-994, 2011.

Dutkay, D., D. Han, Q. Sun, E. Weber. On the Beurling dimension of exponential frames. Advances in Mathematics, 226, 285-297, 2011.

Dutkay, D., D. Han, E. Weber. Bessel sequences of exponentials on fractal measures. Journal of Functional Analysis, 261, 2529-2539, 2011.

Dutkay, D., D. Han, E. Weber. Iterative Approximations of Exponential Bases on Fractal Measures. To appear in Numerical and Functional Analysis and Optimization.

Edholm, C., L. Hogben, M. Hyunh, J. LaGrange, D. Row. Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph. Linear Algebra Applications, In press.

Ekstrand, J., C. Erickson, D. Hay, L. Hogben, J. Roat. Note on positive semidefi nite maximum nullity and positive semidefi nite zero forcing number of partial 2-trees. Electronic Journal of Linear Algebra, 23, 79-87, 2012.

Ellison, E.M., L. Hogben, M. J. Tsatsomeros. Sign patterns that require eventual positivity or require eventual nonnegativity. Electronic Journal of Linear Algebra, 19, 98-107, 2010.

Evans, J.W. Epitaxial thin fi lm growth. SIAM NEWS, November 2010, p.4. Newsjournal of the Society for Industrial & Applied Mathematics (SIAM).

Evans, J.W., P.A. Thiel. A little chemistry helps the big get bigger. Science, 330, 559, 2010.

Fallat, S., L. Hogben. Minimum rank, maximum nullity, and zero forcing number of graphs. To appear in Handbook of Linear Algebra, 2nd Ed.

Fortnow, L., J.H. Lutz, E. Mayordomo. Inseparability and strong hypotheses for disjoint NP pairs. Proceedings of the Twenty-seventhth International Symposium on Theoretical Aspects of Computer Science (STACS 2010, Nancy, France), Schloss Dagstuhl LZI, 395–404, 2010.

Fortnow, L., J.H. Lutz, E. Mayordomo. Inseparability and strong hypotheses for disjoint NP pairs. Invited to appear in Theory of Computing Systems.

Friedland, S., C. K. Li, Y.T. Poon, N. S. Sze. The automorphism group of separable states in quantum information theory. Journal of Mathematical Physics, 52 (4), 2011.

24

Gau, H.L., C. K. Li, Y.T. Poon, N. S. Sze. Quantum error correction and higher rank numerical ranges of normal matrices. SIAM Journal of Matrix Analysis and Applications, 32, 23-43, 2011.

Ghosh, A.P., D. Hay, V. Hirpara, R. Rastegar, A. Roitershtein, A. Schulteis, J. Suh. Random linear recursions with dependent coeffi cients. Statistics & Probability Letters, 80 (21-22), 1597-1605, 2010.

Ghosh, A.P., E. Kleiman, A. Roitershtein. Large deviation bounds for functionals of Viterbi paths. IEEE Transactions on Information Theory 57, 3932-3937, 2011.

Ghosh, A., A. Roitershtein, A. Weerasinghe. Optimal control of a stochastic processing system driven by a fractional Brownian motion input. Advances in Applied Probability, 42 (1), 183-209, 2010.

Ghosh, A., S.M. Ryan, L. Wang, A. Weerasinghe. Heavy traffi c analysis of a simple closed-loop supply chain. Stochastic Models, 26 (4), 549-593, 2010.

Ghosh, A. , A. Weerasinghe. Optimal buffer size and dynamic rate control for a queueing network with reneging in heavy traffi c. Stochastic Processes. and Applications, 120 (11), 2103-2141, 2010.

Giedt, R.J., C. Yang, J.L. Zweier, A. Matzavinos, B.R. Alevriadou. Mitochondrial fi ssion in endothelial cells following simulated ischemia/reperfusion: Role of nitric oxide and mitochondrial reactive oxygen species. Free Radical Biology & Medicine, 52(2), 348–356, 2012.

Gu, X., J.H. Lutz, E. Mayordomo. Curves that must be retraced. Information and Computation, 209, 992–1006, 2011.

Gu, X., J.H. Lutz, S. Nandakumar, J.S. Royer. Axiomatizing resource bounds for measure, models of computation in context. Proceedings of the Seventh Conference on Computability in Europe, (CiE 2011, Sofi a, Bulgaria), Springer, 102–111, 2011.

Gu, X., J.H. Lutz. Effective dimensions and relative frequencies. Theoretical Computer Science, 412, 6696–6711, 2011.

Gunaratne, A., Z. Wu. A Penalty-function method for constrained molecular dynamics simulation. Numerical Analysis and Modeling, 8, 496-517, 2011.

Guo, X., Y. de Decker, J.W. Evans. Metastability in a Schloegl’s second model for autocatalysis: Lattice-gas realization with particle diffusion. Physical Review E, 82, 021121, 2010.

Guo, X., D.K. Unruh, D.-J. Liu, J.W. Evans. Tricriticality in generalized Schloegl models for autocatalysis: Lattice-gas realization with particle diffusion. Physica A, 391, 633-646, 2012.

Haas, R., M. Young. The anti-ramsey number of a perfect matching. Discrete Mathematics, 312, 933-937, 2012.

Hall, H.T., L. Hogben, R. Martin, B. Shader. Expected values of parameters associated with the minimum rank of a graph. Linear Algebra Applications, 433, 101–117, 2010.

Han, Y., D.-J. Liu, B. Unal, F. Qin, D. Jing, C.J. Jenks, P.A. Thiel, J.W. Evans. Formation and coarsening of Ag(110) bilayer islands on NiAl(110): STM analysis and atomistic lattice-gas modeling. Physical Review B, 81, 115462, 2010.

Han, Y., B. Unal, D. Jing, P.A. Thiel, J.W. Evans. Temperature-dependent growth shapes of Ni nanoclusters on NiAl(110). Journal of Chemical Physics, 135, 084706, 2011.

Han, Y., B. Unal, D. Jing, P.A. Thiel, J.W. Evans, D.J. Liu. Quantum islands on metal substrates: Microscopy studies and electronic structure theory. Materials, 3, 3965-3993, 2010. (Special issue on Scanning Probe Microscopy – invited review).

Han, Y., B. Unal, D. Jing, P.A. Thiel, J.W. Evans. Far-from-equilibrium growth on alloy surfaces: Ni and Al on NiAl(110). Physical Review B, 84, 113414, 2011.

Han, Y., J.W. Evans. Atomistic modeling of alloy self-growth by vapor deposition: Ni and Al on NiAl(110). Fall 2011MRS Proceedings Symposium EE (Pittsburgh, 2012).

Hansen, S.W., O. Imanuvilov. Exact control lability of a multilayer Rao-Nakra plate with clamped boundary conditions. ESAIM: Control Optimisation and Calculus Variations, 1101-1132, October 2011.

Hansen, S.W., O. Imanuvilov. Exact control lability of a multilayer Rao-Nakra plate with free boundary conditions. Mathematics of Control and Related Fields (MCRF) 1 (2), 189-230, 2011.

Hansen, S.W., A.O. Ozer. Exact boundary control lability of an abstract Mead-Marcus sandwich beam model. Proceedings of 49th IEEE Conference on Decision and Control (CDC), 2578–2583, Dec 2010.

Hansen, S.W. Book Review: Elementary feedback Stabilization of the linear reaction-convection-diffusion equation and the wave equation by Weijiu Liu, SIAM Review, 53 (2) 388-389, 2011.

Hay, D., R. Rastegar, A. Roitershtein. Multivariate linear recursions with Markov-dependent coeffi cients. Journal of Multivariate Analysis, 102, 521-527, 2011.

Hentzel I., L. Peresi. Special Identities of Bol Algebras. To appear in Linear Algebra and Applications.

Hirsch, R., I. Hodkinson, R.D. Maddux. Weak representations of relation algebras and relational bases. The Journal of Symbolic Logic, 76 ( 03), 870–882, September 2011.

Hogben, L. (with 15 co-authors). Minimum rank of skew-symmetric matrices described by a graph. Linear Algebra Applications, 432, 2457-2472, 2010.

25

Hogben, L., J. McLeod. A linear algebraic view of partition regular matrices. Linear Algebra Applications, 433, 1809–1820, 2010.

Hogben, L. Eventually cyclic matrices and a test for strong eventual nonnegativity. Electronic Journal of Linear Algebra, 19, 129-140, 2010.

Hogben, L. A note on minimum rank and maximum nullity of sign patterns. Electronic Journal of Linear Algebra, 22, 203-213, 2011.

Hogben, L. Editor-in-chief, 2nd edition of Handbook of Linear Algebra (to appear in 2013).

Hogben, L., B. Shader. Maximum generic nullity of a graph. Linear Algebra Applications, 432, 857–866, 2010.

Hogben, L. Minimum rank problems. Linear Algebra Applications, 432, 1961-1974, 2010.

Hou, L.S., J. Lee & H. Manouzi. Finite Element Approximations of Stochastic Optimal Control Problems Constrained by Stochastic Elliptic PDEs. Journal of Mathematical Analysis & Applications. 384, 87-103, 2011.

Hou, L.S., J. Lee. A Robin-Robin Non-Overlapping Domain Decomposition Method for an Elliptic Boundary Control Problem. International Journal of Numerical Analysis & Modeling, 8, 443-465, 2011.

Hryniv, R., P. Sacks. Numerical solution of the inverse spectral problem for Bessel operators. Journal of Computational and Applied Math, 235, 120-136, 2010.

Huang, Y.Q., H. Liu, Y.N. Yu. Recovery of interface derivatives from the piecewise L2 projection. Journal of Computational Physics, 231, 1230-1243, 2012

Huang, Y., Z. Wu. Analysis and simulations of yeast development with an evolutionary game model. Bulletin of Mathematical Biology, DOI: 10.1007/s11538-012-9721-5

Huang, Y., S. Bonett, A. Kloczkowski, R. Jernigan, Z. Wu. P.R.E.S.S. An R-package for exploring residual-level protein structural statistics. To appear in Journal of Bioinformatics and Computational Biology.

Huang, Y., S. Bonett, A. Kloczkowski, R. Jernigan, Z. Wu. Statistical measures on protein residue level structural properties. Journal of Structural and Functional Genomics, 12 (2), 119-136, 2011.

Huang, Y., S. Bonett, A. Kloczkowski, R. Jernigan, Z. Wu, PRESS – A software package for exploring protein residue level structural statistics. Proceedings of BIBIM Workshop on Structural Bioinformatics, Atlanta, Georgia, Nov 2011.

Im, B., J.Y. Ryu, J.D.H. Smith. Sharply transitive sets in quasigroup actions. Journal of Algebraic Combinatorics, 33, 81-93, 2011.

Im, B., J.D.H. Smith. Representation theory for varieties of comtrans algebras and Lie triple systems. International Journal Algebra & Computation, 21, 459-472, 2011.

Indranil, R., G. Luecke, M. Kraeva, J. Coyle. UPC-CHECK: A scalable tool for detecting run-time erros in Unifi ed Parallel C. To apper, Proceedings of International Supercompiting Conference, Hamburg, Germany, 2012.

Jenkins, A., S. Spallone. Local analytic conjugacy of resonant analytic mappings in two variables, in the nonarchimedean setting. To appear, International Journal of Mathematics.

Jing, D., Y. Han, B. Unal, J.W. Evans, P.A. Thiel. Formation of irregular Al islands by room temperature deposition on NiAl(110). MRS Proceedings, 1318, Fall 2010 Symposium UU: Real-time studies of evolving thin fi lms and interfaces and Symposia SS/TT/VV (MRS, Pittsburgh, 2011) mrsf10-1318-uu02-07.

Johnson, K.W., J.D.H. Smith. On the smallest simple, unipotent Bol loop. Journal of Combinatorial Theory Series A, 117 (6), 790-798, 2010.

Johnson, K.W., J.D.H. Smith. Matched pairs, permutation representations, and the Bol property. Communications in Algebra. 38, 2903-2914, 2010.

Kashina, Y., S. Montgomery, R. Ng. On the trace of the antipode and higher indicators. Israel Journal of Mathematics, 2010 (doi: 10.1007/s11856-011-0092-7), arXiv:0910.1628.

Kerby, B., J.D.H. Smith. A graph-theoretic approach to quasigroup cycle numbers. Journal of Combinatorial Theory Series A, 118, 2232-2245, 2011.

Kerby, B., J.D.H. Smith. Quasigroup automorphisms and symmetric group characters. Commentationes Mathematicae Universitatis Carolinae, 51, 279-286, 2010.

Kerby, B., J.D.H. Smith. Quasigroup automorphisms and the Norton-Stein complex. Proceedings of the American Mathematical Society, 138, 3079-3088, 2010.

Lathrop, J.I., J.H. Lutz, B. Patterson. Multi-resolution cellular automata for real computation, Models of computation in context. Proceedings of the Seventh Conference on Computability in Europe (CiE 2011, Sofi a, Bulgaria, June 27–July 2, 2011), Springer, 181–190, 2011.

Lathrop, J.I., J.H. Lutz, M.J. Patitz, S.M. Summers. Computability and complexity in self-assembly. Theory of Computing Systems, 48, 617–647, 2011. (invited paper)

Lee, C., A. Weerasinghe. Convergence of a queueing system in heavy traffi c with general patience-time distributions. Stochastic Processes. and Applications, 121, 2507-2552, 2011. Lee, C., A. Weerasinghe. Stationarity and control of a tandem fl uid network with fractional Brownian motion input. Advances

26

in Applied Probability, 43, 847-874, 2011.

Li, C.K., M. Nakahara, Y.T. Poon, N. S. Sze, H. Tomita. Effi cient quantum error correction for fully correlated noise. Physics Letters A, 375, 3255-3258, 2011.Li, C.K., M. Nakahara, Y.T. Poon, N. S. Sze, H. Tomita. Recovery in quantum error correction for general noise without measurement. Quantum Information and Computation,12, 149-158, 2012. Li, C.K., M. Nakahara, Y.T. Poon, N. S. Sze, H. Tomita. Recursive encoding and decoding of noiseless subsystem and decoherence free subspace. Physics Review A, 84, 044301, 2011.

Li, C.K., Y.T. Poon. Interpolation by completely positive maps. Linear and Multilinear Algebra, 59, 1159-1170, 2011.

Li, C.K., Y.T. Poon. Generalized numerical ranges and quantum error correction, Journal of Operator Theory, 66, 353-384, 2011.

Li, C.K., Y.T. Poon. Sum of Hermitian matrices with given eigenvalues: inertia, rank, and multiple eigenvalues. Canadian Journal of Mathematics, 62 (1), 109-132, 2010. Li, C.K., Y.T. Poon, T. Schulte-Herbruggen. Least-squares approximation by elements from matrix orbits achieved by gradient fl ows on compact lie groups. Mathematics of Computation, 275, 1601-1621, 2011. Li, C.K., Y.T. Poon, N. S. Sze. A note on the realignment criterion. Journal of Physics A, 44, 315304, 2011. Li, C.K., Y.T. Poon, N. S. Sze. Elliptical range theorems for generalized numerical ranges of quadratic operators. Rocky Mountain Journal of Mathematics, 413, 813-832, 2011.

Li, C.K., Y.T. Poon, M. Tominaga. Spectra, norms and numerical ranges of generalized quadratic operators. Linear Algebra and Multilinear Algebra, 59 , 1077-1104, 2011. Li, M., Y. Han, J.W. Evans. Comment on capture zone scaling in island nucleation: Universal fl uctuation behavior. Physical Review Letters, 104, 149601, 2010.

Li, W., C. Yu, A. Carriquiry, W. Kliemann. The asymptotic behavior of the R/S statistic for fractional Brownian motion. Statistics and Probability Letters, 81, 83-91, 2011.

Lieberman, G. M. Asymptotic behavior and uniqueness of blow-up solutions of quasilinear elliptic equations. Journal d’Analyse Mathematique 115, 213-249, 2011.

Lieberman, G. M. Solutions of singular elliptic equations via the oblique derivative problem. Annali dell’Universita di Ferrara, 57, 121-172, 2011.

Lieberman, G. M., X. B. Pan. On a quasilinear equation arising in theory of superconductivity. Proceedings of the Royal Society of Edinburgh 141, 397-407, 2011.

Liu, D.J., H.-T. Chen, Victor S.-Y. Lin, J.W. Evans. Polymer length distributions for catalytic polymerization in mesoporous materials: Non-Markovian behavior associated with partial extrusion. Journal of Chemical Physics, 132, 154102, 2010.

Liu, D.J., J.W. Evans. Interactions between oxygen on Pt(100): Implications for ordering during chemisorption and catalysis. ChemPhysChem, 11 (10), 2174-2181, 2010 (Special Issue: Bunsen Symposium on Microscopic Views of Interface Phenomena - invited).

Liu, D.J., J. Wang, D. Ackerman, I.I. Slowing, M. Pruski, H.-T. Chen, V.S.-Y. Lin, J.W. Evans. Interplay between anomalous transport and catalytic reaction kinetics in single-fi le mesoporous systems. ACS Catalysis, 1, 751-763, 2011 (Memorial Issue for V.S.-Y. Lin).

Liu, D.J., D.M. Ackerman, X. Guo, M.A. Albao, L. Roskop, M.S. Gordon, J.W. Evans. Morphological evolution during growth and erosion on vicinal Si(100) surfaces: From electronic structure to atomistic and coarse-grained modeling. Fall 2011 MRS Proceedings Symposium EE (MRS 2012).

Liu, H., O. Runborg, N. Tanushev. Error estimates for Gaussian beam superpositions. Mathematics of Computation, in press, 2012.

Liu, H., J. Shin. Global well-posedness for the microscopic FENE model with a sharp boundary condition. Journal of Differential Equations. 252 (1), 641-662, 2012.

Liu, H., Z.M. Wang, R. Fox. A level set approach for dilute non-collisional fl uid-particle fl ows. Journal of Computational Physics, 230 (4), 920-936, 2011.

Liu, H., J. Yan. The direct discontinuous Galerkin (DDG) methods for diffusion with interface corrections. Communications in Computational Physics, 8 (3), 541-564, 2010.

Liu, H., Z.Y. Yin. Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Contemporary Mathematics, 526, 274-294, 2011. Also in Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena. Helge Holden and Kenneth H. Karlsen, Editors.

Liu, H., H. Yu. An entropy satisfying fi nite volume method for the Fokker-Planck equation of FENE dumbbell model. To appear in SIAM Journal on Numerical Analysis.

Long, L., J.D.H. Smith. Catalan loops. Mathematical Proceedings of the Cambridge Philosophical Society, 149, 445-453, 2010.

Luecke, G.R., J. Coyle, J. Hoekstra, M. Kraeva, Y. Xu, M.Y. Park, E. Kleiman, O. Weiss, A. Wehe, M. Yahya. The importance of run-time error detection tools for high performance. Proceedings of the 3rd International Workshop on Parallel Tools for High Performance Computing, September 2009, ZIH, Dresden, Springer 2010.

27

Luecke, G.R., O. Weiss, M. Kraeva, J. Coyle, J. Hoekstra. Performance analysis of pure MPI versus MPI+openMP for Jacobi iteration and a 3D FFT on the Cray XT5. Proceedings of the Cray Users Group, Edinburgh, Scotland, May 2010.

Luo, X., Z. Wu. Least-squares approximations in geometric buildup for solving distance geometry problems. Journal of Optimization Theory and Applications 149, 580-598, 2011.

Lutz, J.H. A divergence formula for randomness and dimension. Theoretical Computer Science, 412, 166–177, 2011(invited paper).

Lutz, J.H., B. Shutters. Approximate self-assembly of the Sierpinski Triangle. Programs, Proofs, Processes: Proceedings of the Sixth Conference on Computability in Europe (CiE 2010, Ponta Delgada, Portugal), Springer, 286–295, 2010.

Lutz, J.H., B. Shutters. Approximate self-assembly of the Sierpinski Triangle. To appear (invited paper) in Theory of Computing Systems.

Lutz, R., J. Lutz, J. Lathrop, T. Klinge, E. Henderson, D. Mathur, D. Abo Sheasha. Engineering and verifying requirements for programmable self-assembling nanomachines. Proceedings of the Thirty-fourth International Conference on Software Engineering (ICSE 2012, New Ideas and Emerging Results Track, Zurich, Switzerland, 2012), to appear.

Maddux, R.D. Relevance logic and the calculus of relations. The Review of Symbolic Logic, 3 ( 01), 41-70, March 2010.

Martin, R., B. Stanton. Lower bounds for identifying codes in some infi nite grids. Electronic Journal of Combinatorics, 17(1), 2010.

Matczak, K., A.B. Romanowska, J.D.H. Smith. Dyadic polygons. International Journal of Algebra & Computation, 21, 387-408, 2011.

Mazzuoccolo, G., M. Young. Graphs of arbitrary excessive class. Discrete Mathematics, 311, 32-37, 2011.

Ng, R. A note on Frobenius-Schur indicators. Proceedings of the International Conference on Algebra 2010, 454-560, World Scientifi c, ISBN: 978-981-4366-30-4.

Ng, R. Congruence property and Galois symmetry of modular categories. arXiv:1201.6644.

Ng, R., P. Schauenburg. Congruence subgroups and generalized Frobenius-Schur indicators. Communications in Mathematical Physics, 300 (1), 1-46, 2010.

Nguyen, X.H. Construction of complete embedded self-similar surfaces under mean curvature fl ow II. Advances in Differential Equations, 15 (5-6), 503-530, 2010.

Nguyen, X.H., A. Bennett, T. Moore. A longitudinal study on students' understanding of integration. American Society for Engineering Education Conference Proceedings, 2011, Vancouver, British Columbia, Canada.

Orizaga, S., D.N. Riahi. On combined spatial and temporal instabilities of electrically driven jets with constant or variable applied fi eld. Journal of Theoretical and Applied Mechanics, 50 (1), 301-319, 2012.

Orizaga, S., D.N. Riahi. Resonant instability and nonlinear wave interations in electrically forced jets. Nonlinear Analysis: Real World Applications, 12, 1300-1313, 2011.

Ozer, A.O., S. W. Hansen. Exact control lability of a Rayleigh beam with a single boundary control. Mathematics of Control Signals, 23, 199-222, 2011.

Peters, J.R. Semigroups of locally injective maps and transfer operators. Semigroup Forum, 81 (2), 255–268, 2010.

Preedy, K., P.G. Schofi eld, S. Liu, A. Matzavinos, M. Chaplain, S.F. Hubbard. Modelling contact spread of infection in host-parasitoid systems: vertical transmission of pathogens can cause chaos. Journal of Theoretical Biology. 262 (3): 441-451, 2010.

Rakesh, P. Sacks. Stability for an inverse problem for a two speed hyperbolic PDE in one space dimension. Inverse Problems, 26, 025005, 2010.

Rakesh, P. Sacks. Uniqueness for a hyperbolic inverse problem with angular control on the coeffi cients. Journal of Inverse and Ill-Posed Problems, 9 (1), 107-126, 2011.

Roskop, L., J.W. Evans, M.S. Gordon. Adsorption and diffusion of Gallium Adataoms on the Si(100) -2x1 reconstructed surface: An MCSCF study utilizing surface clusters. Journal of Physical Chemistry C, 115, 23488-23500, 2011.

Saran H., H. Liu. Formulation and analysis of alternating evolution (AE) schemes for hyperbolic conservation laws. SIAM Journal of Scientifi c Computing 33, 3210-3240, 2011.

Schafer, K., S. Kim, A. Matzavinos J. Kuret. 2012, Selectivity requirements for diagnostic imaging of neurofi brillary lesions in Alzheimer's disease: a simulation study. To appear in NeuroImage. DOI: 10.1016/j.neuroimage.2012.01.066

Shen, M., C.J. Jenks, J.W. Evans, P.A. Thiel. How sulfur controls the nucleation of Ag islands on Ag(111). Topics in Catalysis, 54, 83-89, 2011.

Shen, M., C.J. Jenks, J.W. Evans, P.A. Thiel. Rapid decay of vacancy islands at step edges on Ag(111): Step orientation dependence. Journal Physics: Condensed Matter, 22, 215002, 2010.

Sit, A., Z. Wu. Solving a generalized distance geometry problem for protein structure determination. Bulletin of Mathematical Biology, DOI 10.1007/s11538-011-9644-6, 2011.

28

Smiley, M., S. Proulx. Evolution of transcriptional regulation in response to environmental Fluctuations. Journal of Experimental Zoology, Part B, Molecular and Developmental Evolution, 314B, 327-340, 2010.

Smiley, M., S. Proulx. Gene expression dynamics in randomly varying environments. Journal of Mathematical Biology, 61, 231-251, 2010.

Smith, J.D.H. Groups, triality, and hyperquasigroups. Journal of Pure and Applied Algebra, 216, 811-825, 2012.

Smith, J.D.H. Hierarchical information theory and the modeling of biological systems, pp. 419-512 in Biological Information: New Perspectives (eds. R.J. Marks II et al.), Springer Intelligent Systems Reference Library, Berlin, 2012.

Smith, J.D.H. Lambda-rings of automorphisms. Algebra Universalis, 66, 35-48, 2011.

Smith, J.D.H. Modes, modals, and barycentric algebras: a brief survey and an additivity theorem. Demonstratio Mathematica, 44 (3), 571-587, 2011.

Smith, J.D.H. On groups of hypersubstitutions. Algebra Universalis, 64, 39-48, 2010.

Stanton, B. Improved bounds for r-Identifying codes of the hex grid. SIAM Journal of Discrete Mathematics, 25(1), 159-169, 2011.

Thiel, P.A., M. Shen, D.J. Liu, J.W. Evans. Adsorbate-enhanced mass-transport on metal surfaces: oxygen and sulfur on coinage metals. Journal of Vacuum Science Technology A, 28 (6), 1285-1298, 2010. (Invited Review + Journal Cover)

Thiel, P.A., B. Unal, C.Jenks, A. Goldman, P. Canfi eld, T. Lograsso, J.W. Evans, M. Quiquandon, D. Gratias, M. Van Hove. A distinctive feature of the surface structure of quasicrystals: Intrinsic and extrinsic heterogeneity. Israel Journal of Chemistry, 51, 1326-1339, 2011.

Vargas, L.S., H. Verdejo, W. Kliemann. Stability reserve in stochastic linear systems with applications to power systems. Proceedings of PMAPS 2010.

Vedell, P., Z. Wu. A multiple shooting algorithm for solving the boundary value problems in molecular dynamics simulation. To appear in Numerical Analysis and Modeling, 2012.

Vélez, A. Solvability of linear local and nonlocal Robin problems over C(). To appear in Journal of Mathematical Analysis and Applications.Vélez, A. Quasi-linear boundary value problems with generalized nonlocal boundary conditions. Journal of Nonlinear Analysis: Theory, Methods & Applications, 74, 4601-4621, 2011. Verdejo, H., L. Vargas, W. Kliemann. Fine tuning of PSS control [arameters under sustained random perturbations. To appear in IEEE Latin America Transactions.

Wang, J., D. Ackerman, K. Kandel, I.I. Slowing, M. Pruski, J.W. Evans. Conversion reactions in surface-functionalized mesoporous materials: Effect of restricted transport and the catalytic site distribution. Fall 2011 MRS Proceedings Symposium RR (MRS, Pittsburgh, 2012.

Wang, C.J., X. Guo, D.J. Liu, J.W. Evans. Schloegl’s second model for autocatalysis on a cubic lattice: Analysis via mean-fi eld discrete reaction-diffusion equations. Journal of Statistical Physics, 144, 1308-1328, 2011.

Wene, G., I. Hentzel. Albert’s construction for semifi elds of even order. Communications in Algebra, 38 (5), 1790-1795, 2010.

Willson, S.J. Properties of normal phylogenetic networks. Bulletin of Mathematical Biology 72, 340-358, 2010.

Willson, S.J. Regular networks can be uniquely constructed from their trees. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 8, 785-796, 2011.

Willson, S.J. Restricted trees: simplifying networks with bottlenecks. Bulletin of Mathematical Biology, 73, 2322-2338, 2011.

Wu, D., S. Smith, H. Mahan, R. Jernigan, Z. Wu. Analysis of protein dynamics using local DME calculations. International Journal of Bioinformatics Research and Applications, 7, 146-161, 2011.

Wu, D., Z. Wu. Superimposition of protein structures with dynamically weighted RMSD. Journal of Molecular Modeling, 16, 611-622, 2010.

Yan, J. A new nonsymmetric discontinuous Galerkin method for time dependent convection diffusion equations. Journal of Scientifi c Computing, Stanley Osher’s 70th birthday issue. To appear 2012.

Yan, J., S. Osher. A new discontinuous Galerkin method for Hamilton-Jacobi Equations. Journal of Computational Physics, 230 (1), 232-244, 2011.

Zhang, G.P., M. Hupalo, M. Li, C.Z. Wang, J.W. Evans, M.C. Tringides, K.M. Ho. A stochastic coarsening model for Pb islands on the Si(111) surface. Physical Review B. 82, 165414, 2010.

Zhang, M., J. Yan. Fourier type error analysis of the direct discontinuous Galerkin method and its variations for diffusion problems. Journal of Scientifi c Computing, online Nov 2011, DOI:10.1007/s10915-011-9564-5.

Zheng, Z., X. Luo, Z. Wu. A geometric buildup algorithm for the solution of the sensor network localization problem. Mathematical Problems in Engineering, Article ID 927031, 2011.

29

30

Roger Alexander, Associate Professor, Ph.D., 1975, UC-Berkeley. Numerical analysis. alex@iastate.edu

Krishna Athreya, Distinguished Professor, Ph.D., 1967, Stanford. Analysis, probability theory and stochastic processes with emphasis on Markov Chains and applications, branching processes, mathematical statistics. kba@iastate.edu

Maria Axenovich, Associate Professor, Ph.D., 1999, Illinois at Urbana-Champaign. Combinatorics and graphs theory: unavoidable patterns in partitions of combinatorial structures, packing and covering problems, extremal combinatorics. axenovic@iastate.edu

Tathagata Basak, Assistant Professor, Ph.D., 2006, UC-Berkeley. Complex hyperbolic refl ection groups related to Leech lattice and the bimonster, Monster manifold, automorphic forms on hyperbolic spaces, fi nite topological spaces and Poincare duality. tathagat@iastate.edu

Clifford Bergman, Professor & Director of Graduate Education, Ph.D., 1982, UC-Berkeley. Universal algebra, cryptography, steganography, analysis of algorithms. cbergman@iastate.edu

Steve Butler, Assistant Professor, Ph.D., 2008, UC San Diego. Spectral graph theory. combinatorial linear algebra, mathematical juggling, extremal combinatorics. butler@iastate.edu

Rajbir Dahiya, Professor, Ph.D., 1967, Birla Inst. of Tech. & Science (India). Delay, neutral and advanced differential equations, transform theory. rdahiya@iastate.edu

Domenico D’Alessandro, Professor, Ph.D., 1999, UC-Santa Barbara; Ph.D., Universita ‘degli Studi di Padova, Italy. Control theory,

Department of Mathematics tenure and tenure track faculty members with a record of their highest degree and fi elds of interest are listed. Some share appointments with other departments.

mathematical physics and quantum information. daless@iastate.edu

Jennifer Davidson, Associate Professor and Associate Chair, Ph.D., 1989, Florida. Mathematical imaging, steganalysis, stochatic image modeling. davidson@iastate.edu

James W. Evans, Professor, Ph.D., 1979, Adelaide (Australia). Nonequilibrium statistical mechanics and multiscale modeling.Applications include thin fi lm growth, materials science, and reaction-diffusion phenomena.evans@ameslab.gov

Arka Ghosh, Assistant Professor, Ph.D., 2005, NC-Chapel Hill. Stochastic networks and their control, queuing theory with emphasis on heavy traffi c analysis, stochastic modeling of internet/wireless networks, random graphs. apghosh@iastate.edu

Scott Hansen, Associate Professor, Ph.D., 1988, Wisconsin-Madison. Control theory of partial differential equations, elasticity, applied analysis. shansen@iastate.edu

Irvin Hentzel, Professor, Ph.D., 1968, Iowa. Computer algorithms, deterministic and probabilistic for processing algebraic identities. hentzel@iastate.edu

Leslie Hogben, Professor, Ph.D., 1978, Yale. Combinatorial matrix theory, including minimum rank problems, spectra of matrices described by a sign pattern, graph or digraph, matrix completions. Eventually nonnegative matrices and sign patterns. Matrix stability and convergence. lhogben@iastate.edu

L. Steven Hou, Professor, Ph.D., 1989, Carnegie Mellon. Numerical analysis, control theory, partial differential equations, fl uids, math fi nance. stevehou@iastate.edu

Elgin Johnston, Professor & Director, Center for Excellence in Undergraduate Mathematics Education, Ph.D., 1977, Illinois at Urbana-Champaign. Complex analysis, geometric function theory, Faber series expansions on simply connected sets. ehjohnst@iastate.edu

Fritz Keinert, Associate Professor, Ph.D., 1985, Oregon State. Numerical analysis, wavelets, compressed sensing. keinert@iastate.edu

Wolfgang Kliemann, Professor & Chair, Ph.D., 1980, Bremen (Germany). Nonlinear dynamical systems, control systems and stochastic systems with applications in engineering and the life sciences. kliemann@iastate.edu

Gary Lieberman, Professor, Ph.D., 1979, Stanford. Elliptic partial differential equations. lieb@iastate.edu

Hailiang Liu, Professor, Ph.D., 1995, Chinese Academy of Sciences. Applied partial differential equations, numerical analysis. hliu@iastate.edu

Ling Long, Associate Professor, Ph.D., 2002, Pennsylvania State. Number theory and arithmetic geometry. linglong@iastate.edu

Glenn Luecke, Professor, Ph.D., 1970, Caltech. Performance evaluation of high performance computers; parallel computing; Tools for parallel computing; mathematics and high performance computing; parallel linear algebra. grl@iastate.edu

Jack Lutz, Professor, Ph.D., 1987, Caltech. Computational complexity, algorithmic information and randomness, molecular programming and nanoscale self-assembly. lutz@cs.iastate.edu

Roger Maddux, Professor, Ph.D., 1978, UC-Berkeley. Algebra and logic. maddux@iastate.edu

Ryan Martin, Associate Professor, Ph.D., 2000, Rutgers. Extremal and

31

probabilistic combinatorics and graph theory. rymartin@iastate.edu

Anastasios Matzavinos, Assistant Professor, Ph.D., 2004, Dundee (Scotland). Applied mathematics, mathematical biology, data clustering algorithms. tasos@iastate.edu

Siu-Hung Ng, Associate Professor, PhD., 1997, Rutgers. Algebra, representation and tensor category. rng@iastate.edu

Xuan Hien Nguyen, Assistant Professor, Ph. D., 2006, UW-Madison. Geometric analysis, geometric fl ows, elliptic and parabolic differential equations. xhnguyen@iastate.edu

Justin Peters, Professor, Ph.D., 1973, Minnesota. Operator theory, operator algebras. peters@iastate.edu

Yiu Tung Poon, Professor, Ph.D., 1985, UCLA. Quantum information and quantum computation, matrix theory, operator theory, operator algebra. ytpoon@iastate.edu

Alexander Roitershtein, Assistant Professor, Ph.D., 2004, Technion-Israel. Probability theory, stochastic processes. roiterst@iastate.edu

Alric Rothmayer, Professor, Ph.D., 1985, U of Cincinnati. Applied engineering problems in fl uid mechanics using continuum mechanics model development, matched asymptotic and multiple scales asymptotic analysis and computational simulations. Application of three-phase fl ows and aircraft icing.roth@iastate.edu

Paul Sacks, Professor, Ph.D., 1981, Wisconsin-Madison. Partial differential equations, inverse problems. psacks@iastate.edu

Michael W. Smiley, Professor, Ph.D., 1980, Michigan. Partial differential equations, dynamical systems and numerical analysis with applications to cell and systems biology. mwsmiley@iastate.edu

Jonathan Smith, Professor, Ph.D., 1975, Cambridge (England). Combinatorics, algebra and information theory, applications in computer science, physics, biology. jdhsmith@iastate.edu

Sung-Yell Song, Associate Professor, Ph.D., 1987, Ohio State. Algebraic combinatorics: association schemes, designs, graphs. sysong@iastate.edu

Leigh Tesfatsion, Professor, Ph.D., 1975, U of Minnesota. Agent-based computational economics, restructuring of electric power markets, development of agent-based computational laboratories for testing the performance of electric power market designs. tesfatsi@iastate.edu

Moulay Tidriri, Associate Professor, Ph.D., 1992, Paris IX (Dauphine). Mathematical physics, numerical analysis, scientifi c computing. tidriri@iastate.edu

Zhi Jian Wang, Professor, Ph.D., 1990, Glasgow. Computational fl uid dynamics; Cartesian, Chimera and other grid methods; higher order methods for unstructured grids; numerical simulation including turbulence and transitions; parallel computing. zjw@iastate.edu

Eric S. Weber, Associate Professor, Ph.D., 1999, Colorado. Harmonic

analysis with applications; wavelet, frame, and sampling theory. esweber@iastate.edu

Ananda Weerasinghe, Professor, Ph.D., 1986, Minnesota. Stochastic processes, queueing networks in heavy traffi c, mathematics of fi nance. ananda@iastate.edu

Stephen Willson, University Professor, Ph.D., 1973, Michigan. Phylogenetic trees and networks, fractals, and game theory. swillson@iastate.edu

James A. Wilson, Associate Professor & Undergraduate Coordinator, Ph.D., 1978, Wisconsin-Madison. Special functions, orthogonal polynomials, combinatorial sums.jawilson@iastate.edu

Zhijun Wu, Professor, Ph.D., 1991, Rice. Numerical linear algebra and optimization, numerical solutions of ordinary and partial differential equations, bioinformatics and computational biology. zhijun@iastate.edu

Jue Yan, Assistant Professor, Ph.D., 2002, Brown. Numerical analysis, high order fi nite element discontinuous Galerkin methods. Application to computational fl uid dynamics and computational math biology. jyan@iastate.edu

Department of Mathematics396 Carver HallAmes, Iowa 50011

Research Highlights 2012Editor: Sue Ellen Tuttletuttle@iastate.edu 515-294-8680

Send address corrections to: Records Department ISU Foundation 2505 Elwood Drive Ames, IA 50010-8644or: recordsstaff@foundation.iastate.edu