Mathematics Commons^™

Hybrid Multiscale Landmark And Deformable Image Registration, Dana C. Paquin, Doron Levy, Lei Xing

Mathematics

An image registration technique is presented for the registration of medical images using a hybrid combination of coarse-scale landmark and B-splines deformable registration techniques. The technique is particularly effective for registration problems in which the images to be registered contain large localized deformations. A brief overview of landmark and deformable registration techniques is presented. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese, A multiscale image representation using hierarchical (BV,L²) decompositions, Multiscale Modeling and Simulations, vol. 2, no. 4, pp. 554-579, 2004, is reviewed, and an image registration algorithm is developed based on …

Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani

Faculty Research and Creative Activity

We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is any abelian subgroup of orientation preserving $C^1$ diffeomorphisms of $S^2$ then there is a common fixed point for all elements of a subgroup of $F$ with index at most two.

Solution To Problem 1751, A Combinatorial Identity, Arthur T. Benjamin, Andrew Carman '09

All HMC Faculty Publications and Research

A combinatorial proof to Iliya Bluskov's proposed Problem 1751.

A Hyperbolic Two -Step Model Based Finite Difference Method For Studying Thermal Deformation In A Micro Thin Film Heated By Ultrashort -Pulsed Lasers, Tianchan Niu

Doctoral Dissertations

Heat transport through micro thin films plays a very important role in microtechnology applications. Many microelectronic devices have metal thin films as their key components. Microscale heat transfer is also important for the thermal processing of materials, including laser micromachining, laser patterning, laser synthesis and laser surface hardening. Hence, studying the thermal behavior of thin films is essential for predicting the performance of a microelectronic device or for obtaining the desired microstructure. Recently, it has become very popular to use ultrashort-pulsed lasers in thermal processing, which lasers have pulse durations of the order of subpicoseconds to femtoseconds, and these kinds …

How Geometer’S Sketchpad Improves Student Learning, William George Awe

Mathematics Graduate Theses

This study investigated whether dynamic software improves learning and reviews different types of dynamic software. The study then narrows its focus to one type of dynamic software, Geometer’s Sketchpad and studies how Geometer’s Sketchpad, in itself, improves student learning. The researcher identified what dynamic software is, the importance of dynamic software and different types of dynamic software. The researcher also identifies how dynamic software is utilized in schools and researches how to improve the use of dynamic software in schools. Dynamic software, and Geometer’s Sketchpad, In particular, was found to improve learning across grade levels and with different levels of …

A Universal Theory Of Pseudocodewords, Nathan Axvig, Emily Price, Eric T. Psota, Deanna Turk, Lance C. Pérez, Judy L. Walker

Department of Mathematics: Faculty Publications

Three types of pseudocodewords for LDPC codes are found in the literature: graph cover pseudocodewords, linear programming pseudocodewords, and computation tree pseudocodewords. In this paper we first review these three notions and known connections between them. We then propose a new decoding rule — universal cover decoding — for LDPC codes. This new decoding rule also has a notion of pseudocodeword attached, and this fourth notion provides a framework in which we can better understand the other three.

A Software-Based Trust Framework For Distributed Industrial Management Systems, Sheikh Iqbal Ahamed, Mohammad Zulkernine, Steve Wolfe

Mathematics, Statistics and Computer Science Faculty Research and Publications

One of the major problems in industrial security management is that most organizations or enterprises do not provide adequate guidelines or well-defined policy with respect to trust management, and trust is still an afterthought in most security engineering projects. With the increase of handheld devices, managers of business organizations tend to use handheld devices to access the information systems. However, the connection or access to an information system requires appropriate level of trust. In this paper, we present a flexible, manageable, and configurable software-based trust framework for the handheld devices of mangers to access distributed information systems. The presented framework …

Promoting Mathematical Communication And Community Via Blackboard, Kris H. Green, Erica L. Johnson

Mathematical and Computing Sciences Faculty/Staff Publications

Major changes in mathematics pedagogy include writing as pedagogy and the role of community in learning. The classroom community is naturally extended by the use of online discussion boards. In this paper several models for student use of online discussion boards that have been successfully used to promote mathematical discourse are presented. Structured and unstructured examples that are easily adaptable and transportable to a variety of mathematics classroom settings are offered. These assignments facilitate student engagement and interaction outside of the classroom. Assessment, utility, and transferability are offered. Although the authors use the discussion boards provided by Blackboard, this particular …

Some Open Questions On Modulo Classes, Frank J. Palladino

Senior Honors Projects

No abstract provided.

Semilinear Spdes As Dynamical Systems (Mittag-Leffler Institute Seminar), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

A Better Definition Of The Kilogram, Ronald F. Fox, Theodore P. Hill

Research Scholars in Residence

Fixing the value of Avogadro's constant, the number of atoms in 12 grams of carbon-12, at exactly 84446886³ would imply that one gram is the mass of exactly 18x14074481³ carbon-12 atoms. This new definition of the gram, and thereby also the kilogram, is precise, elegant and unchanging in time, unlike the current 118-year-old artifact kilogram in Paris and the proposed experimental definitions of the kilogram using man-made silicon spheres or the watt balance apparatus.

Anticipating Semilinear Spdes (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Unfolding Restricted Convex Caps, Joseph O'Rourke

Computer Science: Faculty Publications

This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restrictions: the cap’s faces are quadrilaterals, with vertices over an underlying integer lattice, and such that the cap convexity is "radially monotone," a type of smoothness constraint. Extensions of Cauchy’s arm lemma are used in the proof of non-overlap.

Transport Schemes On A Sphere Using Radial Basis Functions, Natasha Flyer, Grady Wright

Mathematics Faculty Publications and Presentations

The aim of this work is to introduce the physics community to the high performance of radial basis functions (RBFs) compared to other spectral methods for modeling transport (pure advection) and to provide the first known application of the RBF methodology to hyperbolic partial differential equations on a sphere. First, it is shown that even when the advective operator is posed in spherical coordinates (thus having singularities at the poles), the RBF formulation of it is completely singularity-free. Then, two classical test cases are conducted: 1) linear advection, where the initial condition is simply transported around the sphere and 2) …

Mathematical Analysis Of Pde Systems Which Govern °Uid Structure Interactive Phenomena, George Avalos, Roberto Triggiani

Department of Mathematics: Faculty Publications

In this paper, we review and comment upon recently derived results for time dependent partial differential equation (PDE) models, which have been used to describe the various fluid-structure interactions which occur in nature. For these fluid-structure PDEs, this survey is particularly focused on the authors' results of (i) semigroup wellposedness, (ii) stability, and (iii) backward uniqueness.

Asymptotic Behavior Of The Global Attractors To The Boussinesq System For Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the global attractors to the Boussinesq system for Rayleigh-Bénard convection converge to that of the infinite-Prandtl- number model for convection as the Prandtl number approaches infinity. This offers partial justification of the infinite-Prandtl-number model for convection as a valid simplified model for convection at large Prandtl number even in the long-time regime. © 2006 Wiley Periodicals, Inc.

Evaluation Maps In Rational Homotopy, Yves Felix, Gregory Lupton

Mathematics and Statistics Faculty Publications

In the rational category of nilpotent complexes, let E be an H-space acting on a space X. With mild hypotheses we show that the action on the base point w: E→X factors through a map ΓE:SE→X, where S E is a finite product of odd-dimensional spheres and Γ E is a homotopy monomorphism. Among others, the following consequences are obtained:π∗(w)6=0 if and only if w is essential and H∗(w)6=0 if and only if X satisfies a strong splitting condition.

Necessary Conditions For Super Minimizers In Constrained Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

This paper concerns the study of the so-called super minimizers related to the concept of super efficiency in constrained problems of multiobjective optimization, where cost mappings are generally set-valued. We derive necessary conditions for super minimizers on the base of advanced tools of variational analysis and generalized differentiation that are new in both finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives.

Self-Assembled Biomimetic Antireflection Coatings, Nicholas C. Linn, Chih-Hung Sun, Peng Jiang, Bin Jiang

Mathematics and Statistics Faculty Publications and Presentations

The authors report a simple self-assembly technique for fabricating antireflection coatings that mimic antireflective moth eyes. Wafer-scale, nonclose-packed colloidal crystals with remarkable large hexagonal domains are created by a spin-coating technology. The resulting polymer-embedded colloidal crystals exhibit highly ordered surface modulation and can be used directly as templates to cast poly(dimethylsiloxane) (PDMS) molds. Moth-eye antireflection coatings with adjustable reflectivity can then be molded against the PDMS master. The specular reflection of replicated nipple arrays matches the theoretical prediction using a thin-film multilayer model. These biomimetic films may find important technological application in optical coatings and solar cells.

Paving Hessenberg Varieties By Affines, Julianna S. Tymoczko

Mathematics Sciences: Faculty Publications

Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology, geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent Hessenberg varieties for all classical types, generalizing results of De Concini-Lusztig-Procesi and Kostant. This paving is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties have no odd-dimensional homology.

3d Simulation Of Cracks And Fractures In A Molecular Solid Under Stress And Compression, Mark Korlie

Department of Mathematics Faculty Scholarship and Creative Works

Using molecular mechanics, we study the evolution and propagation of cracks and fractures in a three-dimensional molecular sheet of ice under stress and compression. We use an approximate 6-12 Lennard-Jones potential for a pair of ice molecules to derive dynamical equations for the ice molecules in the solid. The resulting systems of nonlinear ordinary differential equations are then used to simulate the evolution and propagation of cracks and fractures in the solid. In the computer examples, we compare dynamical responses when the solid sheet of ice has a slot or does not have a slot. The mechanisms for development of …

Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung

School of Mathematical & Statistical Sciences Faculty Publications

In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally $\alpha$-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one "energy''-like and one "enstrophy''-like. In a finite inertial range there are in general two spectral fluxes, one associated with each conserved quantity. We derive here an inequality comparing the relative magnitudes of the "energy'' and "enstrophy'' fluxes for finite or infinitesimal dissipations, and for hyper or hypo viscosities. When this inequality is satisfied, as is the case of 2D turbulence,where the energy flux contribution to the energy spectrum is small, the subdominant part will be effectively hidden. …

Environmental Kuznets Curve: Some Econometric Analyses., Soumyananda Dinda Dr.

Doctoral Theses

This dissertation explores some issues of environmental economics and development. A concept crystallizing in the development and environmental economics literature is the notion that socioeconomic and environmental measures follow predictable paths associated with growing per capita income. In this context, the nature of relationship between economic development and environmental quality has become the focus of increasing attention. The issue of whether environmental degradation increases monotonically, decreases monotonically, or at first increases and then declines along a country’s development path, has critical implications for policy. Whilst development through industrialization brings higher incomes and well-being, this seems to act as a magnifier …

The Power Of Strong Fourier Sampling: Quantum Algorithms For Affine Groups And Hidden Shifts, Cristopher Moore, Daniel Rockmore, Alexander Russell, Leonard J. Schulman

Dartmouth Scholarship

Many quantum algorithms, including Shor’s celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which an unknown subgroupH of a group G must be determined from a quantum state ψ over G that is uniformly supported on a left coset of H. These hidden subgroup problems are typically solved by Fourier sampling: the quantum Fourier transform of ψ is computed and measured. When the underlying group is nonabelian, two important variants of the Fourier sampling paradigm have been identified: the weak standard method, where only representation names are measured, and the strong standard method, …

Some Necessary Conditions Of Boolean Functions To Resist Algebraic Attacks., Deepak Dalai Dr.

Doctoral Theses

No abstract provided.

Construction Of (Hierarchical) Identity-Based Encryption Protocols Using Bilinear Pairing., Sanjit Chatterjee Dr.

Doctoral Theses

Science, it is argued [65], advances through paradigm shifts. Concepts emerge that open-up new vistas of research, fundamentally changing the way we are used to looking at things. Between these paradigm shifts remain the periods of consolidation. Periods when human mind explores the newly found territory, shedding light on hitherto unknown dimensions. If radical changes are the hallmarks of paradigm shifts, the period within witnesses small but continuous developments, occasionally marked by its own milestones. It is in these periods that human faculty tries to grasp the full significance of the new concepts, consolidates its gains and thereby pushes the …

Game-Theoretic View On Intermediated Exchange, Thomas Grassl

Dissertations, Master's Theses and Master's Reports - Open

Intermediaries permeate modern economic exchange. Most classical models on intermediated exchange are driven by information asymmetry and inventory management. These two factors are of reduced significance in modern economies. This makes it necessary to develop models that correspond more closely to modern financial marketplaces. The goal of this dissertation is to propose and examine such models in a game theoretical context.

The proposed models are driven by asymmetries in the goals of different market participants. Hedging pressure as one of the most critical aspects in the behavior of commercial entities plays a crucial role.

The first market model shows that …

The Discrete Logarithm Problem And Ternary Functional Graphs, Max F. Brugger, Christina A. Frederick

Mathematical Sciences Technical Reports (MSTR)

Encryption is essential to the security of transactions and communications, but the algorithms on which they rely might not be as secure as we all assume. In this paper, we investigate the randomness of the discrete exponentiation function used frequently in encryption. We show how we used exponential generating functions to gain theoretical data for mapping statistics in ternary functional graphs. Then, we compare mapping statistics of discrete exponentiation functional graphs, for a range of primes, with mapping statistics of the respective ternary functional graphs.

Decompositions, Packings, And Coverings Of Complete Directed Gaphs With A 3-Circuit And A Pendent Arc., Chrys Gwellem

Electronic Theses and Dissertations

In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K₃ ∪ {e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.

Tricyclic Steiner Triple Systems With 1-Rotational Subsystems., Quan Duc Tran

Electronic Theses and Dissertations

A Steiner triple system of order v, denoted STS(v), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this thesis we give necessary and sufficient conditions for the existence of a tricyclic STS(v) when one of the cycles is of length one. In this case, the STS(v) will contain a subsystem which admits an automorphism consisting of a fixed point and a single cycle. The subsystem is said to be 1-rotational.