The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

An Interactive Theorem Prover for First-Order Dynamic Logic

Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs. The method of proving correctness of properties of a computer program using the well-known Hoare Logic can be implemented by utilizing the robustness of dynamic logic. For a very broad range of languages and applications in program veri cation, a theorem prover named KIV (Karlsruhe Interactive Veri er) Theorem Prover has already been developed. But a high degree of automation and its complexity make it di cult to use it for educational purposes. My research work is motivated towards the design and implementation of a similar interactive theorem prover with educational use as its main design criteria. As the key purpose of this system is to serve as an educational tool, it is a self-explanatory system that explains every step of creating a derivation, i.e., proving a theorem. This deductive system is implemented in the platform-independent programming language Java. In addition, a very popular combination of a lexical analyzer generator, JFlex, and the parser generator BYacc/J for parsing formulas and programs has been used.

Confocal and two-photon microscopy : image enhancement /

Confocal and two-photon microcopy have become essential tools in biological research and today many investigations are not possible without their help. The valuable advantage that these two techniques offer is the ability of optical sectioning. Optical sectioning makes it possible to obtain 3D visuahzation of the structiu-es, and hence, valuable information of the structural relationships, the geometrical, and the morphological aspects of the specimen. The achievable lateral and axial resolutions by confocal and two-photon microscopy, similar to other optical imaging systems, are both defined by the diffraction theorem. Any aberration and imperfection present during the imaging results in broadening of the calculated theoretical resolution, blurring, geometrical distortions in the acquired images that interfere with the analysis of the structures, and lower the collected fluorescence from the specimen. The aberrations may have different causes and they can be classified by their sources such as specimen-induced aberrations, optics-induced aberrations, illumination aberrations, and misalignment aberrations. This thesis presents an investigation and study of image enhancement. The goal of this thesis was approached in two different directions. Initially, we investigated the sources of the imperfections. We propose methods to eliminate or minimize aberrations introduced during the image acquisition by optimizing the acquisition conditions. The impact on the resolution as a result of using a coverslip the thickness of which is mismatched with the one that the objective lens is designed for was shown and a novel technique was introduced in order to define the proper value on the correction collar of the lens. The amoimt of spherical aberration with regard to t he numerical aperture of the objective lens was investigated and it was shown that, based on the purpose of our imaging tasks, different numerical apertures must be used. The deformed beam cross section of the single-photon excitation source was corrected and the enhancement of the resolution and image quaUty was shown. Furthermore, the dependency of the scattered light on the excitation wavelength was shown empirically. In the second part, we continued the study of the image enhancement process by deconvolution techniques. Although deconvolution algorithms are used widely to improve the quality of the images, how well a deconvolution algorithm responds highly depends on the point spread function (PSF) of the imaging system applied to the algorithm and the level of its accuracy. We investigated approaches that can be done in order to obtain more precise PSF. Novel methods to improve the pattern of the PSF and reduce the noise are proposed. Furthermore, multiple soiu'ces to extract the PSFs of the imaging system are introduced and the empirical deconvolution results by using each of these PSFs are compared together. The results confirm that a greater improvement attained by applying the in situ PSF during the deconvolution process.

The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.

Bradley Institute of Music fonds

1.23 m. textual records, 1 col. post card, 1 b&w post card, 116 col. photographs, 59 b&w photographs, 6 negatives, 1 metal logo, 2 photo cuts, 7 woodcuts, 1 VHS tape, 1 stamp/press, 1 guest book, 5 account books

Honey proteins and their interaction with polyphenols

This project aimed to determine the protein prof i les and concent rat ion in honeys, ef fect of storage condi t ions on the protein content and the interact ion between proteins and polyphenols. Thi r teen honeys f rom di f ferent botanical or igins were analyzed for thei r protein prof i les using SDS-PAGE, protein concent rat ion and phenol ic content , using the Pierce Protein Assay and Fol in-Ciocal teau methods, respectively. Protein-polyphenol interact ions were analyzed by a combinat ion of the ext ract ion of honeys wi th solvents of di f ferent polar i t ies fol lowed by LCjMS analysis of the obtained f ract ions. Results demonst rated a di f ferent protein content in the tested honeys, wi th buckwheat honey possessing the highest protein concent rat ion. We have shown that the reduct ion of proteins dur ing honey storage was caused, partially, by the protein complexat ion wi th phenolics. The LCjMS analysis of the peak elut ing at retent ion t ime of 10 to 14 min demonst rated that these phenolics included f lavonoids such as Pinobanksin, Pinobanksin acetate, Apigenin, Kaemferol and Myricetin and also cinnamic acid.

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Temple Grandin fonds, 1974-2006 (non-inclusive)

Temple Grandin was born in Boston, Massachusetts on August 29,1947 to Richard Grandin and Eustacia Cutler. She was diagnosed with autism at age 2. She suffered from delayed speech development and did not begin to speak until the age of 4. Temple’s mother defied the doctors and kept her out of institutions. Temple was given speech therapy as well as an intensive education. Her high school science teacher and her aunt on a ranch in Arizona inspired Temple to continue her studies and pursue a career as a scientist and livestock equipment designer.She graduated from Hampshire Country School (a boarding school for gifted children) in Ridge, New Hampshire in 1966, and earned a bachelor’s degree in psychology from Franklin Pierce College in 1970. In 1975, she received a master’s degree in animal science from Arizona State University and then a doctoral degree in animal science from the University of Illinois in 1989. She is currently a professor at Colorado State University. Dr. Grandin is one of the world’s leaders in the design of livestock handling facilities. She has done extensive work in design of handling facilities for animals and has developed animal welfare guidelines for the meat industries. Dr. Grandin is a past member of the board of directors of the Autism Society of America. She lectures to parents and teachers throughout the U.S. on her experiences with autism. She makes the case that the world needs people on the autism spectrum: visual thinkers, pattern thinkers and verbal thinkers. Some of Temple Grandin’s books include: Animals Make Us Human, Animals in Translation, The Way I See It, The Autistic Brain, and Different…Not Less. In 2010, a movie entitled “Temple Grandin” starring Clare Danes was released. The movie was based on Grandin’s own writings. Temple Grandin is an expert on animal behavior, a bestselling author, and an autism activist. In 2010, she was listed in the “Heroes” category in the “Time” list of the world’s 100 most influential people. She has received numerous awards including an honorary doctorate from McGill, the University of Illinois and Duke University. Temple Granin is a philosophical leader of both the animal welfare and autism advocacy movements. sources: http://www.templegrandin.com/ http://en.wikipedia.org/wiki/Temple_Grandin

Edge-choosability of Planar Graphs

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.

A Handbook for Ontario J/I Pre-Service Teachers Developing Inclusive Pedagogy: Understanding Pre-Service Teachers' Thoughts and Feelings About Diversity

This project presents a handbook for Ontario Junior/Intermediate (J/I) pre-service teachers, Ontario J/I teacher education instructors, and J/I associate teachers that facilitates the identification, analysis, and reorganization of J/I pre-service teachers’ thoughts and feelings about diversity characteristics to develop inclusive teaching pedagogy. The handbook outlines collaborative and independent learning activities designed for integration into compulsory J/I Bachelor of Education (B.Ed.) program courses, practicum placements, and independent reflective situations. The handbook is composed of 5 sections: (a) Rationale for Importance; (b) Cross-Curricular Activities for J/I B.Ed. Courses; (c) Course-Specific Activities; (d) Practicum Placement Activities; and (e) Resources for Inclusive Educators. A critical content analysis of a 2011-2012 J/I B.Ed. program in Ontario enabled the creation of the handbook to address specific teacher education programming focused on helping pre-service teachers understand their thoughts and feelings about diversity for the development of inclusive teaching pedagogy. This research contributes to the advancement of theory and practice regarding development of teacher education programming that promotes J/I pre-service teachers’ inclusive pedagogy.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.

New conserved vorticity integrals for moving surfaces in multi-dimensional fluid flow

For inviscid fluid flow in any n-dimensional Riemannian manifold, new conserved vorticity integrals generalizing helicity, enstrophy, and entropy circulation are derived for lower-dimensional surfaces that move along fluid streamlines. Conditions are determined for which the integrals yield constants of motion for the fluid. In the case when an inviscid fluid is isentropic, these new constants of motion generalize Kelvin’s circulation theorem from closed loops to closed surfaces of any dimension.