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ItemSubdivisions of complete graphs(Georgia Institute of Technology, 20170523) Wang, Yan ; Yu, Xingxing ; Peng, Richard ; Tetali, Prasad ; Thomas, Robin ; Warnke, Lutz ; MathematicsA subdivision of a graph G, also known as a topological G and denoted by TG, is a graph obtained from G by replacing certain edges of G with internally vertexdisjoint paths. This dissertation studies a problem in structural graph theory regarding subdivisions of a complete graph in graphs. In this dissertation, we focus on TK_5, or subdivisions of K_5. A well known theorem of Kuratowski in 1932 states that a graph is planar if, and only if, it does not contain a subdivision of K_5 or K_{3,3}. Wagner proved in 1937 that if a graph other than K_5 does not contain any subdivision of K_{3,3} then it is planar or it admits a cut of size at most 2. Kelmans and, independently, Seymour conjectured in the 1970s that if a graph does not contain any subdivision of K_5 then it is planar or it admits a cut of size at most 4. In this dissertation, we give a proof of the KelmansSeymour conjecture.

ItemFirstprinciples study of the hydrogenmetal system(Georgia Institute of Technology, 199305) Wang, Yan ; Chou, MeiYin ; Physics

ItemAsymptotic theory for decentralized sequential hypothesis testing problems and sequential minimum energy design algorithm(Georgia Institute of Technology, 20110519) Wang, Yan ; Mei, Yajun ; Ji, Chuanyi ; Shapiro, Alexander ; Vengazhiyil, Roshan Joseph ; Wu, C. F. Jeff ; Industrial and Systems EngineeringThe dissertation investigates asymptotic theory of decentralized sequential hypothesis testing problems as well as asymptotic behaviors of the Sequential Minimum Energy Design (SMED). The main results are summarized as follows. 1.We develop the firstorder asymptotic optimality theory for decentralized sequential multihypothesis testing under a Bayes framework. Asymptotically optimal tests are obtained from the class of "twostage" procedures and the optimal local quantizers are shown to be the "maximin" quantizers that are characterized as a randomization of at most M1 Unambiguous Likelihood Quantizers (ULQ) when testing M >= 2 hypotheses. 2. We generalize the classical KullbackLeibler inequality to investigate the quantization effects on the secondorder and other generalorder moments of loglikelihood ratios. It is shown that a quantization may increase these quantities, but such an increase is bounded by a universal constant that depends on the order of the moment. This result provides a simpler sufficient condition for asymptotic theory of decentralized sequential detection. 3. We propose a class of multistage tests for decentralized sequential multihypothesis testing problems, and show that with suitably chosen thresholds at different stages, it can hold the secondorder asymptotic optimality properties when the hypotheses testing problem is "asymmetric." 4. We characterize the asymptotic behaviors of SMED algorithm, particularly the denseness and distributions of the design points. In addition, we propose a simplified version of SMED that is computationally more efficient.

ItemSoundbased image and positon recognition system: SIPReS(Georgia Institute of Technology, 201806) Uno, Shin’ichiro ; Suzuki, Yasuo ; Watanabe, Takashi ; Matsumoto, Miku ; Wang, Yan ; International Community for Auditory Display ; Nihon Fukushi University. Department of Human Care Engineering ; Shouei Denshi Kenkyusyo Ltd.,Co.We developed software called SIPReS, which describes twodimensional images with sound. With this system, visuallyimpaired people can tell the location of a certain point in an image just by hearing notes of frequency each assigned according to the brightness of the point a user touches on. It can run on Android smartphones and tablets. We conducted a smallscale experiment to see if a visuallyimpaired person can recognize images with SIPReS. In the experiment, the subject successfully recognized if there is an object or not. He also recognized the location information. The experiment suggests this application’s potential as image recognition software.