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## Ph.D. Candidates Receive Hoods From Their Thesis Advisors

Tim Carnes, Yinan Huang, Jie Chen, Baldur Magnusson and Tuohua Wu, wearing their newly placed hoods. |

In a tradition of long standing, six doctor of philosophy graduates had hoods added to their commencement garb by their thesis advisors as a central part of the 2010 ORIE graduation ceremony in Schwartz Auditorium on the Cornell campus. Three came to graduate work at Cornell with undergraduate degrees from Chinese universities, one from Stetson University in Florida, one from Harvey Mudd College in California, and one from Cornell's Department of Mathematics.

In the ceremony, Professor David Shmoys introduced the candidates and their dissertation advisors with a brief description, based on input from the students and their advisors,of the research that was carried out to earn the degree.

Professor David Shmoys congratulates Dr. Tim Carnes |

#### Tim Carnes

Tim Carnes' thesis is called *Approximation Algorithms Via the Primal-dual Schema: Applications of the Simple dual-ascent method to Inventory, Routing, and Assignment Problems*. In it he devises new computationally efficient algorithms for a number of important problems in logistics, ranging from inventory management and medical air transport scheduling to work-load balancing.

Such combinatorial optimization problems cannot be effectively solved by brute force methods in which all possible alternative allocations are enumerated by a computer and compared in terms of cost in order to determine the best, or optimal, solution. Even methods which, for example, iterate through candidate allocations making successive improvements in value (ascent methods) usually can not be guaranteed to get anywhere close to an optimal solution. Hence the aim for a given class of such problems is to design an algorithm that quickly produces a solution that, while not necessarily optimal, is still provably not much worse.

Carnes' thesis, according to his advisor Shmoys, "contains an elegant mathematical approach to deriving such approximation algorithms and provides algorithms with this sort of performance guarantee." The approach relies on ascent methods that work simultaneously on the ("primal") mathematical formulation of the problem and on a derived or 'dual' problem. In one part of the thesis Carnes applies this approach to problems that arose from work with a company that manages a fleet of airplanes used to transport medical patients to hospitals and needs each day to devise a schedule for the next day's non-urgent-care cases. Moreover he applies it to a longer range planning problem in which bases for the airplanes are located in such a way as to minimize flight costs over time.

Carnes, a graduate of Harvey Mudd College in California, has begun work as a postdoctoral fellow at MIT's Sloan School of Management.

Professor Peter Jackson and Dr. Jie Chen. |

#### Jie Chen

Maintaining an effective level of inventory of replacement parts in a repair system is a difficult challenge, especially if the size of orders received by the emergency stocking location is random. In her thesis, *Lost Sales and Emergency Order Systems under Stuttering Poissson Demand*, completed under the guidance of Professor Peter Jackson, Jie Chen has solved the problem of planning such stock levels. Chen, a graduate of Peking University, has derived formulas to predict the level of customer service that can be expected from any combination of stock levels, and has derived practical algorithms to optimize these stock levels.

In carrying out her analysis, Chen makes use of a fundamental result from a seminal paper published in 1966 by mathematicians at the RAND Corporation and General Electric. In the process she discovered an error in that paper which had been unchallenged for 40 years.

Shmoys said of Chen's work that "the results will be useful to companies such as Xerox in achieving high customer service with minimal inventory investment." Chen has accepted a position as an Operations Research Analyst at the AT&T Shannon Lab in Florham Park, NJ, which is a successor to units of Bell Laboratories, where Operations Research has been an active research area for nearly 50 years.

Professor Martin Wells and Dr. Yinan Huang |

#### Yinan Huang

Yinan Huang, an electrical engineering graduate of Tsinghua University in China, wrote *Recursive Bayesian Methods for Sequential Parameter-State Estimation* under the guidance of Professor Martin Wells. Professor Wells is in the Department of Statistical Science and the School of Industrial and Labor Relations, and is a member of the Field of Operations Research.

Bayesian methods in statistics employ a formula developed in the eighteenth century by Reverend Thomas Bayes that enables the successive refinement of estimates of a probability distribution as data are accumulated. Shmoys noted that "traditional Bayesian methods face significant challenges" when the underlying statistical models are not based on the Gaussian (i.e. bell curve) distribution and/or entail a large number of variables. Huang developed a general approach to updating the estimates of the probability distribution when the state of the underlying phenomenon is subject to diffusion and "jumps" (discontinuities).

The idea behind Huang's work is the decomposition of the joint distribution of a large number of variables into much more tractable parts, using what are known as Variational Bayes methods. Within this framework, he developed procedures for sequentially estimating the state of a system and for determining the parameters of the formulas that govern it. The result is a unified approach to a family of problems ranging from financial time series to the analysis of DNA and other genomic sequences.

Huang will join Morgan Stanley in New York City as an associate desk strategist in the Securitized Products Group.

Professor Bruce Turnbull congratulates Dr. Baldur Magnusson |

#### Baldur Magnusson

Baldur Magnusson, a citizen of Iceland who plays hockey and the violin, wrote *Targeted Therapies: Adaptive Sequential Designs for Subgroup Selection* under the guidance of Professor Bruce Turnbull. This thesis applies to the design of randomized, placebo-controlled (i.e. "double blind") clinical trials, the "gold standard" in medical experimentation.

As Shmoys pointed out in his remarks, picking the appropriate strategy in designing clinical trials involves a "multi-million dollar decision." Often, there is a choice between concentrating the trials on a subset of patients who may benefit most from the new therapy being tested, or aiming for a general population of patients with the hope that all could benefit. The concentrated approach would be more likely to lead to quick and successful results, but there may be no way to know if they are applicable to the broader population and therefore how valuable further development would be. Moreover, it may be difficult to recruit a large enough subset of patients. The alternative of aiming for a general population may dilute the effect and lead to a negative conclusion.

In his thesis, Magnusson develops a new statistical methodology for the construction of designs that can be adapted as the trial progresses, for example by starting with a large population, reviewing the results at interim points in the course of the trial (by carefully 'unblinding' to an independent monitoring panel), and making a decision as to whether to continue with only a subset of the population. Such an adaptive design introduces statistical challenges, such as correcting for selection bias and preserving the false positive error rate while maintaining efficiency and savings on the size of the sample.

Magnusson came to Cornell from Stetson University, where he held a music scholarship. His thesis advisor is Prof. Bruce Turnbull, who has been quoted in The Scientist magazine and The Wall Street Journal as expressing caution that appropriate statistical methods be used in the adaptive design of clinical trials.

Dr. Tuohua Wu and Professor Martin Wells. |

#### Tuohua Wu

The analysis of the risk associated with financial assets has come to center stage in the world economy in recent years. Wu's dissertation is a contribution to the statistical analysis of the risk that the issuer of a financial instrument such as a bond will default, i.e. fail to make an interest or principal payment, go bankrupt, or require the the instrument be exchanged for one of lesser value. Over time, such defaults have been shown to occur in clusters that are not fully explained by common macroeconomic and firm-specific information.

Wu's dissertation, *Modeling Multi-period Corporate Defaults: Macro, Contagion and Frailty Effects in Default Clustering*, decomposes the risk of default into three factors in order to explain the clustering of defaults. One of these factors, routinely taken into account in financial analysis, is the exposure of firms to common macroeconomic factors. Another is the tendency of defaults, and especially bankruptcies, to be contagious due the impact that a default by one firm has on other firms that have business relationships with it. A third, called frailty, summarizes additional, latent components that may only be revealed after the fact, such as reduced trust in the accuracy of public accounting information. Wu analyzed data on defaults and showed that including contagion and frailty factors results in a good characterization of historical default clustering, without which the probability of extreme events leading to large portfolio loss will be underestimated.

In his remarks, Shmoys noted that "Wu's dissertation is the first application of a statistical estimation procedure called efficient method of moments (EMM) procedure in the credit risk arena." EMM uses computational simulation to match observed properties of the data to properties - moments - of the predicted probability distribution. Shmoys added that Wu's "empirical findings can be used by banks and credit portfolio managers for economic capital calculations and risk evaluation of protfolio credit derivatives."

Wu, who is a graduate of Tsinghua University, has accepted a position as an Associate at Citgroup in New York City. His research was conducted under the guidance of Professor Martin Wells.

Professor Gennady Samorodnitsky and Dr. Sami Umut Can. |

#### Sami Umut Can

Sami Umut Can completed his thesis under the supervision of ORIE professor Gennady Samorodnitsky. Can, who is affiliated with Cornell's Center of Applied Mathematics, wrote on *Some Convergence Results on Stable, Infinite Moving-average Processes and Stable Self-similar Processes*. His dissertation develops results for "heavy-tailed" models that are "fast becoming more and more important in many areas of application, ranging from telecommunication network traffic to finance," Shmoys said.

Infinite moving-average processes arise as the consequence of random variation in a weighted series of observations, such as security prices, that accumulates over time. Internet traffic, which has very different properties from the telephone traffic that once served as the basis for the design of telecommunications networks, has been found to yield processes that behave the same at various time scales, hence are self-similar. In both examples, observed values are more concentrated at extreme values than would be predicted by the normal distribution, or bell curve, hence the phenomena are called "heavy-tailed."

Can determined that certain such systems, characterized by random changes determined by random probabilities and resulting in random costs or payoffs, converge to a limiting process that can be represented in terms of Brownian motion (in some sense the simplest form of random process). In the words of Ward Whitt, ORIE Ph.D. '69. such limiting processes "are interesting and important because they generate simple approximations for complicated stochastic processes and because they help explain the statistical regularity associated with a macroscopic view of uncertainty." Hence mathematical results about them, such as Can developed, are useful in the design of networks and in financial analysis.

In his dissertation Can, who came to Cornell as an undergraduate from Istanbul, Turkey, also showed how commonly used methods to break down data from light-tailed time-dependent phenomena into combinations of periodic processes (as is done in Fourier analysis) behave for heavy-tailed phenomena. He will join EURANDOM, the European Institute for Statistics, Probability, Stochastic Operations Research and its Applications, in Eindhoven, the Netherlands as a postdoctoral fellow.

Not present at the ceremony were Arijit Chakrabarthy and Alexander Erdelyi, who received their Ph.D. degrees in January, 2010.