Equilibrium Points of an AND-OR Tree: under Constraints on Probability

We study a probability distribution d on the truth assignments to a uniform binary AND-OR tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed the following: If d achieves the equilibrium among independent distributions (ID) then d is an independent identical distribution (IID). We show a stronger form of the above result. Given a real number r such that 0 < r < 1, we consider a constraint that the probability of the root node having the value 0 is r. Our main result is the following: When we restrict ourselves to IDs satisfying this constraint, the above result of Liu and Tanaka still holds. The proof employs clever tricks of induction. In particular, we show two fundamental relationships between expected cost and probability in an IID on an OR-AND tree: (1) The ratio of the cost to the probability (of the root having the value 0) is a decreasing function of the probability x of the leaf. (2) The ratio of derivative of the cost to the derivative of the probability is a decreasing function of x, too.Comment: 13 pages, 3 figure

Liu, Mengxiong

University of Michigan, Ann Arbor, MI, School of Informational & Library Studies, Ph.D., 1990 University of Denver, Denver, CO, Graduate School of Librarianship & Information Management, M.L.S., 1983 International Studies University, Shanghai, China, English Department, B.A., 1968https://scholarworks.sjsu.edu/erfa_bios/1273/thumbnail.jp

Breach procedure for axillary hyperhidrosis.

Dear Editor, We read with interest the communication on ‘A simple and practical method for axillary osmidrosis resection’ by Liu X, Mao T, Lei Z, Fan D appeared on JPRAS 2009.1 We found the description of the technique very useful with the support of intra-operative pictures. The use of artery clips to evert the skin flaps can be easily reproduced. However it is surprising that the Authors did not consider and mention in the References a paper by Mr N Breach appeared in the Annals of the Royal College of Surgeons of England in the late 70ies,2 when he was Senior Registrar at the Plastic Surgery Department of the Queen Victoria Hospital, East Grinstead, UK. Since then this latter procedure for surgical treatment of axillary hyperhidrosis has been widely adopted, [3], [4] and [5] especially in the Western world and in the UK where is known as the ‘Breach’ procedure. The main difference with the technique described in the paper by Liu X et al. consists in the number of incisions that has now been minimized

Osteoinductive and Antibacterial Biomaterials for Bone Tissue Engineering

Wismeyer, D. [Promotor]Liu, Y. [Copromotor

Angiogenesis in Bone: Implications for Bone Tumor Therapy and Bone Tissue Engineering

Wismeyer, D. [Promotor]Hunziker, E.B. [Promotor]Liu, Y. [Copromotor]Hofstetter, W. [Copromotor

Some molecule-based materials low dimension nanostructures

Molecule based materials nanoarchitectures have been employed as important nanoscale building blocks for advanced materials and smart miniature devices to fulfill the increasing needs of high materials usage efficiency. Different dimension molecule based materials based nanoarchitectures, especially low dimension nanostructures, attract significant attention due to its fascinating controlled structure and functionality-easy tailoring with excellent semi-conductive properties and stability. In this report, we discuss the some molecule based materials self-assembled oriented functional nanoarchitectures by coordinated inducing. The molecular material building blocks, aggregate structures and their properties in optical, electrical and photoelectrical properties were shown. REFERENCES [1] Guo, Y.B.; Xu, L.; Liu, H. B.; Li, Y. J.; Che, C.-M.; Li, Y. L. Adv. Mater. 2015, 27, 985. [2] Li, Y. J.; Liu, T. F.; Liu, H. B.; Tian, M.-Z.; Li, Y. L. Acc. Chem. Res., 2014, 47,1186. [3] Li, Y. J.; Liang Xu, Liu, H. B.; Li, Y. L. Chem. Soc. Rev. 2014, 43, 2572. [4] Liu, H. B.; Xu, J. L.; Li, Y. J.; Li, Y. L. Acc. Chem. Res. 2010, 43, 1496. [5] Zheng, H. Y.; Li, Y. J.; Liu, H. B.; Yin, X. D.; Li, Y. L. Chem. Soc. Rev. 2011, 40, 4506

NAREA AWARDS

Awards: Outstanding Master's Thesis Award The Distinct Impact of Food Stamps on Food Spending: Comparing Evidence from Economic Theory, Policy Experiments, and Non-Linear Regression Methods, by Parke E. Wilde Master's Thesis Award of Merit Economic Analysis of Different Herbicide Treatment Recommendations for Groundwater Protection, by Wei Liu Master's Thesis Award of Merit Implications of Changing European Union Trade Policies on Latin America's Trade in Bananas, by Kleber Machado Journal Article of the Year for 1995 Recreation Swimming Benefits of New Hampshire Lake Water Quality Policies, by Michael Needleman and Mary Jo Kealy Honorary Life Member Award: Olan D. Forker Distinguished Member Award: Conrado "Bobby" Gempesaw IITeaching/Communication/Extension/Profession,

Explicit eigenvalues of certain scaled trigonometric matrices

In a very recent paper "\emph{On eigenvalues and equivalent transformation of trigonometric matrices}" (D. Zhang, Z. Lin, and Y. Liu, LAA 436, 71--78 (2012)), the authors motivated and discussed a trigonometric matrix that arises in the design of finite impulse response (FIR) digital filters. The eigenvalues of this matrix shed light on the FIR filter design, so obtaining them in closed form was investigated. Zhang \emph{et al.}\ proved that their matrix had rank-4 and they conjectured closed form expressions for its eigenvalues, leaving a rigorous proof as an open problem. This paper studies trigonometric matrices significantly more general than theirs, deduces their rank, and derives closed-forms for their eigenvalues. As a corollary, it yields a short proof of the conjectures in the aforementioned paper.Comment: 7 pages; fixed Lemma 2, tightened inequalitie