Campuses:

<span class=strong>Reception and poster session</span>

Friday, November 3, 2006 - 5:15pm - 6:30pm
Lind 400
  • Undergraduate, graduate, and postdoctoral opportunities

    at New York University

    Margaret Wright (New York University)
    New York University, located in the heart of Greenwich
    Village in New York City, offers outstanding undergraduate,
    graduate, and postdoctoral opportunities. Material about
    all of these, especially those involving the Courant Institute
    of Mathematical Sciences, will be available, and the presenter
    will be happy to answer questions.
  • The fixed charge network flow problem
    Adewale Faparusi (Texas A & M University)
    The fixed charge network flow problem (FCNFP) is NP Hard and has
    various practical applications including transportation, network design,
    communication, and production scheduling. More work has been done on the
    development of algorithms for specific variants of the FCNFP than the
    generalized problem.
    Various formulations and exact and heuristic methods for solving the FCNFP
    are reviewed.
  • Modelling faculty teaching workload as a linear program
    Kanadpriya Basu (University of South Carolina)Maria Cristina Villalobos (University of Texas Pan American)
    We present an assignment problem that distributes classes among instructors
    in the Mathematics department. Currently, the Director of Scheduling assigns
    about 190 classes 60 instructors using the manual process of trial-and-error
    by considering, for example, an instructor's teaching workload and class
    preferences. However, this process is quite time-consuming. Therefore, we
    model the problem as a linear program with binary variables. The results are
    presented for Fall'2006.
  • Mathematical modelling at NIST: An example
    Fern Hunt (National Institute of Standards and Technology)
    Fluorescent stains and dyes are widely used to visualize biological structure
    and function on the cellular and sub-cellular level. The photodegradation of
    fluorescent particles (fluorophores) is an extremely important issue for
    biomedical and biotechnology applications because the sensitivity and the
    accuracy of the quantitative information conveyed by assays using them
    depends on fluorophore photostability.
    Recently the presenter and Dr. Adolfas Gaigalas of NIST developed a
    mathematical model of an experimental method for measuring photodegradation.
    The model is a set of coupled partial differential equations that describe
    the kinetics of photodegradation and the flow of fluorophores through the
    experimental apparatus. Using singular perturbation techniques, the
    model is reduced to to a
    dramatically simpler and experimentally accessible ordinary differential
    equation. The latter can be used to interpret and fit the experimental
    meausurements, thus providing a quantitative characterization of photostability.
  • Optimal product portfolio formulation: Merging predictive data mining

    with analytical target cascading

    Conrad Tucker (University of Illinois at Urbana-Champaign)
    This paper addresses two important fundamental areas in product
    family
    formulation that have recently begun to receive great
    attention. First is the
    incorporation of market demand that we address through a data
    mining
    approach where realistic customer survey data is translated
    into performance
    design targets. Second is platform architecture design that we
    model as a
    dynamic entity. The dynamic approach to product architecture
    optimization
    differs from conventional static approaches in that a
    predefined architecture is
    not present at the initial stage of product design, but rather
    evolves with
    fluctuations in customer performance preferences. The benefits
    of direct
    customer input in product family design will be realized
    through our cell phone
    product family example presented in this work. An optimal
    family of cell phones
    is created with modularity decisions made analytically at the
    enterprise level that
    maximize company profit.
  • Existence of traveling waves solution for a nonlocal

    reaction-diffusion model of influenza A

    Joaquin Rivera (The University of Iowa)
    In this paper we study the existence of traveling wave solutions
    for an integro-differential system of equations. The system was proposed by
    Lin et. al as a model for the spread for influenza A drift. The model uses
    diffusion to simulate the mutation of the virus along a one dimensional
    phenotype space. By considering the system under the traveling wave variable
    *z=x-ct* the PDE system is transformed to a higher dimensional ODE
    system. Applying
    the theory of geometric singular perturbation we constructed a traveling
    wave solution for the system.

    Key words: traveling wave, reaction-diffusion, geometric singular
    perturbation.
  • Large circuit pairs in matroids
    Bryan Williams (Hampton University)
    Scott Smith conjectured in 1979 that two distinct longest
    cycles of
    a k-connected graph meet in at least k vertices when k is less
    than or equal
    to 2.
    This conjecture is known to be true for k is less than or equal
    to 10. Only
    the case
    k less than or equal to 6 appears in the literature, however.
    Reid and Wu
    generalized Smith's conjecture to k-connected matroids by
    considering largest circuits. The case k=2 of the matroid
    conjecture follows from a result of Seymour. In addition,
    McMurray,
    Reid, Sheppardson, Wei, and Wu established an extension of the
    matroid conjecture for k=2 and proved it for cographic
    matroids
    when k ≤ 6. In his Ph.D. dissertation, McMurray established
    the
    matroid conjecture for matroids of circumference four. I
    establish
    Reid and Wu's conjecture for several classes of matroids which
    include those that have connectivity three, circumference
    five, and
    spanning circuits, Along with some structured results for
    connectivity four. I am also looking at extending the dual
    result
    of Grotschel and Nemhauser's established result of Smith's
    conjecture for k less than or equal to 6, by considering
    largest bonds in
    graphs.
  • Automated parameter estimation and sensitivity analysis
    Carlos Quintero Salazar (University of Texas)
    We present the computational issues that will be considered
    for the implementation of hybrid optimization approaches oriented to
    automated parameter estimation problems. The proposed hybrid
    optimization approaches are based on the coupling of the Simultaneous
    Perturbation Stochastic Approximation (SPSA) approach (a global and
    derivative free optimization method) and a globalized Newton-Krylov
    Interior Point algorithm (NKIP) (a global and derivative dependent
    optimization method). The first coupling will imply the generation of
    a metamodel that will allow to incorporate derivative information on a
    simpler representation of the original problem. The second type of
    coupling assumes that there is some derivative information available
    but its utilization is postponed until the SPSA algorithm has made
    sufficient progress toward the solution. We implement the hybrid optimization
    approach on a simple testcase, and present some numerical results.
  • Historical development of the secant method: from the

    Babylonians to Wolfe

    Joanna Papakonstantinou (Rice University)
    Many believe the Secant Method arose out of the finite difference
    approximation of the derivative in Newton's Method. However,
    historical evidence reveals that the Secant Method predated Newton's
    Method. It was originally referred to as the Rule of Double False
    Position and dates back to the Babylonians. We present a historical
    development of the Secant Method in 1-D. We introduce the definition
    of general position, present the n+1 point interpolation idea, and
    outline Wolfe's formulation to compute the basic secant
    approximation. We explain how the method is numerically unstable,
    because it leads to ill-conditioning due to the deterioration of
    general positioning.
  • Reduced basis simulation
    Rachel Vincent-Finley (Rice University)
    Molecular dynamics (MD) simulation provides a powerful tool to study
    molecular motion with respect to classical mechanics. When considering
    protein dynamics, local motions, such as bond stretching, occur within
    femtoseconds, while rigid body and large-scale motions, occur within a
    range of nanoseconds to seconds. Generally to capture motion at all
    levels using standard numerical integration techniques to solve the
    equations of motion requires time steps on the order of a femtosecond.
    To date, literature reports simulations of solvated proteins on the
    order of nanoseconds, however, simulations of this length do not provide
    adequate sampling for the study of large-scale molecular motion.

    In this presentation we will describe a method for performing molecular
    simulations with respect to a reduced coordinate space. Given a standard
    MD trajectory we use principal component analysis (PCA) to identify k
    dominant characteristics of a trajectory and construct a k-dimensional
    (k-D) representation of the atomic coordinates with respect to these k
    characteristics. Using this model we define equations of motion and
    perform simulations with respect to the constructed k-D representation.

    We apply our method to test molecules and compare the simulations to
    standard MD simulations of the molecules. Our method allows us to
    efficiently simulate test molecules by reducing the storage and the
    computation requirements. The results indicate that the molecular
    activity with respect to our simulation method is comparable to that
    observed in the standard MD simulations of these molecules.
  • An epidemiological approach to the spread of minor

    political parties

    Daniel Romero (Arizona State University)
    Third political parties are influential in shaping American politics. In this work
    we study the spread of
    third parties ideologies in a voting population where we assume that party members
    are more
    influential in recruiting new third party voters than non-member third party voters
    (i.e., those who vote
    but do not pay party dues, officiate, campaign). The study is conducted using a
    ‘Susceptible-Infected’
    epidemiological model with a system of nonlinear ordinary differential equations as
    applied to a case
    study, the Green Party. Through the analysis of our system we obtain the party-free
    and member-free
    equilibria as well as two endemic equilibria, one of which is stable. We consider
    the conditions for
    existence and stability (if applicable) of all equilibria and we identify two
    threshold parameters in our
    model that describe the different possible scenarios for a third political party and
    its spread. Of the
    two possible endemic states for the voting population we posit ideal threshold
    ranges for which the
    stable endemic equilibrium exists. Interestingly enough, our system produces a
    backward bifurcation
    that identifies parameter values under which a third party can either thrive or die
    depending on the
    initial number of members in the voting system. We then perform sensitivity
    analysis to the threshold
    conditions to isolate those parameters to which our model is most sensitive. We
    explore all results
    through numerical simulations and refer to data from the Green Party in the state of
    Pennsylvania as a
    case study for parameter estimation.
  • Fourier restriction problem and its relation to PDE

    No Abstract
  • Mathematical Sciences Research Institute
    Kathleen O'Hara (Mathematical Sciences Research Institute)
    Come learn about opportunities at MSRI.
  • Thermal stability of a reactive third grade fluid in a cylindrical pipe: An

    exploitation of Hermite-Padé approximation technique

    Oluwole Makinde (University of Limpopo)
    A large class of real fluids used in industries is chemically reactive and
    exhibit non-Newtonian characteristics e.g. coal slurries, polymer solutions or
    melts, drilling mud, hydrocarbon oils, grease, etc. Because of the non-linear
    relationship between stress and the rate of strain, the analysis of the behavior of
    such fluids tends to be more complicated and subtle in comparison with that of
    Newtonian fluids. In this paper, we investigate the thermal stability of a reactive
    third-grade fluid flowing steadily through a cylindrical pipe with isothermal wall.
    It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting
    the consumption of the material. Approximate solutions are constructed for the
    governing nonlinear boundary value problem using regular perturbation techniques
    together with a special type of Hermite-Padé approximants and important properties
    of the flow structure including bifurcations and thermal criticality conditions are
    discussed.
  • Change in host behavior and its impact on the co-evolution of

    dengue

    David Murillo (Arizona State University)
    The joint evolutionary dynamics of dengue strains are poorly understood
    despite its high prevalence around the world. Two dengue strains are put in
    competition in a population where behavioral changes can affect the
    probability of infection. The destabilizing dynamic effect of even minor
    behavioral changes are discussed and their role in dengue control is explained
  • Texas prefreshman engineering program: Closing the

    gap for minorities in science and engineering

    Manuel Berriozábal (University of Texas)
    The Texas Prefreshman Engineering Program (TexPREP) started in
    the summer of 1979 at the University of Texas at San Antonio.
    It is a seven-to eight week summer mathematics-based academic
    enrichment program designed to prepare middle school and high
    school students for college studies in science and engineering.
    The program focuses on the development of abstract reasoning
    and problem solving skills through the mastery of academic
    content. Since the program started, over 24,000 students have
    completed at least one summer component of PREP. At least 75%
    of the students have come from minority groups underrepresented
    in science and engineering and over 50% have been women. Of
    the 11,000 students former students who are of college age,
    6,500 responded to the 2005 annual survey. The following is a
    summary of the results:

    • 99.9% graduated from high school;
    • 97 % are college
      students (3,300) or senior college graduates (3,000);

    • The senior college graduation rate is 80%;
    • 78% of the
      college graduates are underrepresented minorities;

    • 50% of the college graduates are science, mathematics, or
      engineering majors;

    • 74% of the science, mathematics, and engineering graduates
      are underrepresented minorities.


    The 2006 Program served over 2600 students in 21 Texas college
    campuses and 6 college campuses in other states and Puerto
    Rico.
  • Differential elimination of PDEs by numerical algebraic

    geometry and numerical linear algebra

    Wenyuan Wu (University of Western Ontario)
    The computational difficulty of completing nonlinear PDE to involutive form by
    differential elimination algorithms is a significant obstacle in applications.
    We apply numerical methods to this problem which, unlike existing symbolic
    methods for exact systems, can be applied to approximate systems arising in
    applications.

    We use Numerical Algebraic Geometry to process the lower order leading
    nonlinear parts of such PDE systems to obtain their witness sets. To check the
    conditions for involutivity Numerical Linear Algebra techniques are applied to
    constant matrices which are the leading linear parts of such systems evaluated
    at the generic points. Representations for the constraints result from applying
    a method based on Polynomial Matrix Theory. Examples to illustrate the new
    approach are given.

    This is joint work with Greg Reid. The paper is available at
    publish.uwo.ca/~wwu26
  • Mathematics and its application to modeling the earth's surface
    Diana Dalbotten (University of Minnesota, Twin Cities)
    Students with a Mathematics or Physics degree who wish to
    apply their abstract skills in a concrete way are invited to
    investigate the National Center for Earth-surface Dynamics. This
    multidisciplinary center examines the Earth's surface
    quantitatively, using computer models, field studies, and laboratory
    experiments to investigate channels and channel dynamics.
  • AWM Mentor Network
    Rachel Kuske (University of British Columbia)
    At present, the goal of the Association for Women in Mathematics (AWM)
    Mentor Network is to match mentors, both men and women, with girls and women who are interested in mathematics or are pursuing careers in mathematics. The network is intended to link mentors with a variety of groups: recent PhD's, graduate students, undergraduates, high school and grade school students, and teachers. Matching is based on common interests in careers in academics or industry, math education, balance of career and family, or general mathematical interests. Following increased support from the math institutes, we are considering the possibility to expand the Mentor Network to other under-represented groups in mathematics. All who are interested in participating in this expansion are encouraged to discuss this possibility at the conference.
  • A new semifield of order 36
    Minerva Cordero-Epperson (University of Texas)
    A (finite) semifield is a non-associative division ring; the associated projective
    plane is called a semifield plane. The first semifields were defined by Dixon in the
    early 1900s; in the 1960s several new classes were introduced including the twisted
    fields defined by Albert. In this poster we will give a historical development of
    finite semifields. We will present the development in the last decade including a
    new semifield recently constructed by the author.
  • Professional Science Masters programs
    Sheila Tobias (NONE)
    Why Industry should be interested in PSM

    Companies are transforming their cultures and reshaping their business models to focus on high-impact innovation. This business strategy requires a skill set very different from the old Six Sigma. Universities have responded to this challenge by creating a new business and industry-oriented Professional Science (Mathematics) Masters degree (PSM).
    PSM degree holders are trained to work productively at what Business Week calls the sweet spot where design, customer understanding, and emerging technologies come together.
    PSM graduates have expertise in science, mathematics, and computational skills PLUS business basics, project management, regulatory affairs, technology transfer, teamwork, and communication.

    Why Students should be interested in PSM

    A two-year post-graduate terminal degree for mathematics/computational science majors, in areas of applied mathematics, including financial mathematics, industrial mathematics, computational science and at the intersection of disciplines including bioinformatics, proteomics, environmental decision making, biostatistics, statistics for entrepreneurship, and applications of GIS.

    For more information, see www.sciencemasters.com.
  • Error estimates between the stochastic simulation algorithm (SSA) and

    the tau-leap method

    Josue Noyola-Martinez (Rice University)
    The use of the relatively new tau-leap algorithm to model the kinematics of
    genetic regulatory systems is of great interest, however, the algorithm's
    accuracy is not known. We introduce a new method which enables us to establish
    the accuracy of the tau-leap method effectively. Gillespie introduced both the
    Stochastic Simulation Algorithm (SSA) and the tau-leap method to simulate
    chemical systems which can model the dynamics of cellular processes. The SSA
    is an exact method but is computationally inefficient. The tau-leap is an
    approximate method which has computational advantages over the SSA. There have
    been some efforts to quantify the error between the SSA and the tau-leap
    method, but the accuracy of these efforts is questionable. We propose an
    adaptation of a non-homogeneous Poisson process to couple the SSA and tau-leap
    so that we can make direct comparisons between individual realizations of their
    simulations. Our method has not been attempted in the literature and we
    demonstrate that it gives far better error estimates than anything proposed
    previously.
  • JHU Applied Physics Lab - Aviation systems engineering group overview
    Javier Armendariz (Johns Hopkins University)
    The Aviation Systems Engineering Group at JHU/APL conducts systems
    engineering and analysis to support the development and operational
    employment of military aviation systems. In this endeavor technical
    requirements and enabling technologies are identified that relate to
    operational requirements and operational concepts. The group strives to
    maintain expertise in air defense threat characterization and analyze
    the survivability and effectiveness of current and future military
    aviation systems. To this end we are involved in a wide array of
    projects encompassing many technical disciplines.
  • American Institute of Mathematics
    Rachel Kuske (University of British Columbia)
    AIM, the American Institute of Mathematics, would like to bring to your attention opportunities at its conference center, AIM Research Conference Center (ARCC). Located in Palo Alto, California, AIM has been hosting fully-funded, week-long workshops at ARCC in all areas of the mathematical sciences since 2002. Through ARCC, AIM supports and develops an innovative style of workshop that encourages interactive research as part of the workshop, fosters new connections, and builds productive and lasting collaborations. Several proactive approaches are used to attract a diverse groups of participants, including women and under-represented minorities as well as junior mathematicians. All 32 participants receive full funding to attend the week-long workshop.
  • Research Institute of Mathematical Sciences
    Luis Enrique Carrillo Díaz (Universidad Nacional Mayor de San Marcos)Roxana Lopez-Cruz (Universidad Nacional Mayor de San Marcos)
    The Research Institute of Mathematical Sciences develops
    research in pure and applied mathematics, statistics,
    computer science and research operations. One of the goals
    of the Institute is to promote means of international
    cooperation to support the research among the members of
    our institute and other insitutions of the world.
    PESQUIMAT is the review of the Institute in charge to spread
    the research of our members.
    http://matematicas.unmsm.edu.pe/
  • Mathematical aspects of dopamine's turnover
    David Tello (Arizona State University)
    What do the world's champion Muhammad Ali and A Beautiful Mind's John
    F. Nash have in common? They both suffer from dopamine malfunction
    in one of the major dopaminegic pathways. It is believed that loss
    of dopamine activity in the nigrostriatal pathway is associated with
    Parkinson's Disease and that an imbalance of dopamine activity in the
    mesocortical\mesolimbic pathway is the cause of (positive\negative)
    symptoms of Schizophrenia.

    I have assembled a collection of available literature concerning
    dopamine turnover (the cascade chemical process that takes place in
    the terminal button) and some of the available mathematical models
    describing the dopamine process. This collection constitutes a
    foundation of future work. I plan to develop a stochastic model
    describing the dopamine cascade in the different major dopaminergic pathways.



  • Discriminant analysis based on statistical depth

    functions

    Asheber Abebe (Auburn University)
    We will consider the problem of identifying the most likely source
    of a multivariate data point from among several multivariate
    populations. The use of statistical depth functions for solving
    this classification problem will be discussed. Statistical depth functions
    provide a center-outward ordering of points in a multivariate data
    cloud and hence can be considered to be multivariate analogues of ranks.
    Specifically, classification through maximizing the estimated
    transvariation probability of statistical depths is proposed. Considering
    elliptically
    symmetric populations, it will be illustrated that these new
    classification techniques provide lower misclassification error rates in
    the case of heavy tailed distributions.

    This is joint work with Nedret Billor, Asuman Turkmen and Sai Nudurupati.

  • Accurate computation of second order derivatives using complex

    variables

    Nelson Butuk (Prairie View A&M University)
    In this presentation, the complex variables method of computing accurate
    first derivatives is combined with an approximation method to calculate
    second order derivatives efficiently. The complex variables method, is some
    what similar to the automatic differentiation technique using the popular
    software tool ADIFOR, to obtain sensitivities (derivatives) from source
    codes. Application of automatic differentiation to an existing source code,
    (that evaluates output functions) automatically generates another source
    code that can be used to evaluate both output functions and derivatives of
    those functions with respect to specified code input or internal
    parameters. The pre-compiler software tool, ADIFOR is usually used to
    obtain derivatives from CFD and grid generation codes. On the other hand,
    the complex variables (CV) approach is simpler and easier to implement. The
    current implementation of CV method only computes first order derivatives
    accurately. The current methods of computing 2nd order derivatives using
    different approaches are based on construction of appropriate meshes in a
    given domain. Then some form of Taylor expansion scheme is applied to these
    meshes to obtain the desired derivatives. The problem with this approach is
    that only the function is continuous across meshes, but not its partial
    derivatives. Because of this, the computed 2nd order derivatives are
    usually inaccurate. The new method to be presented will address this issue
    by combining the CV method with an accurate efficient approximation method.
  • Progress report on the NSA mathematics enhancement grant:

    Developing a mathematics culture among undergraduate

    mathematics majors at North Carolina A&T State University

    Janis Oldham (North Carolina Agricultural and Technical State University)
    From July 1, 1998 - September 30, 2001 North Carolina A&T's Math Department conducted a project, funded through the National Security Agency. The project was designed to produce a core of undergraduate students having a “mathematics culture”, that is, a depth in proof based higher mathematics, the ability to articulate ideas, solve problems, and conduct inquiry and research. It was hoped this core would communicate its knowledge and experience on to successive classes of students, maintaining this newly developed culture. It was also originally hoped that the Math department would go on to develop an Honors program from this program, or at least incorporate the main program elements, especially the required problem sessions. Students not having developed in such a 'culture' meant not being prepared to do well in graduate school or have the expertise to work in government or industry.

    The current state of affairs is that the culture did not persist. While the department did adopt 2 program elements, namely a freshman / new math major orientation course, and a required problem session with the Logic/Proof transitions course, university administrative edicts and university curriculum changes, impeded or gutted the effectiveness of those program elements. Nevertheless 72% of those who were in the program for 1, 2, or 3 years graduated with a degree in mathematics, applied mathematics, or mathematics education from an accredited institution. This included 3 who went on to earn Ph.D.'s, and many more who earned masters degrees. These students had gpa's from 2.5 through just under 4.0. Students who currently hold these gpa's are not developing as the students did during the period of the NSA grant. What we believe is that the specific intervention and high amount of contact hours with students, with the purpose of compelling, guiding, and developing the appropriate study discipline, made the difference. For such results to persist, designing methods to maintain the intervention until a math culture actually takes hold, is necessary.
  • Statistical and Applied Mathematical Sciences Institute
    Christopher Jones (University of North Carolina, Chapel Hill)
    Come learn about opportunities at SAMSI.
  • Lawrence Livermore National Laboratory
    Steven Lee (Lawrence Livermore National Laboratory)
    Come learn about the exciting opportunities in the Computation Directorate
    at LLNL.
  • Nonlinear interaction of light in disordered optical fiber arrays
    Alejandro Aceves (University of New Mexico)
    Light propagation in coupled fiber arrays is described by a balanced of
    diffraction and nonlinearity. At
    high intensities, light is localized as a nonlinear mode propagating in a
    few fibers. The imperfections
    in the manufacturing of such fiber arrays account for multiplicative noise
    in the governing equations.
    Here we analyze how this noise affects the phenomenon of linear
    (Anderson-like) and nonlinear localization.
  • Algebraic characterizations of some classes of quasi-cyclic

    codes

    Isaac Woungang (Ryerson Polytechnical University)
    The so-called Jensen's concatenation function has been found to be a
    powerful tool for the study of quasi-cyclic (QC) codes, and in general,
    of codes invariant under a permutation. In this paper, we introduce two
    novel applications of the aforementioned tool. First, we provide a trace
    description of a 1-generator QC code, which generalizes the well-known
    trace description of a cyclic code. Second, we provide an algebraic
    characterization of QC codes obtained as q-ary images of qm-ary
    irreducible cyclic codes. These QC codes are shown to be decomposable
    into the direct sum of a fixed number of irreducible components. Based upon
    this decomposition, we obtain some lower bounds on the minimum distances
    of some classes of such codes. Our numerical results show that our technique
    can yield optimal linear codes.
  • Spherical nilpotent orbits of reductive Lie groups: an overview
    Donald King (Northeastern University)
    The vector space of complex symmetric n×n matrices is preserved by
    conjugation with complex n×n orthogonal matrices. Conjugacy classes
    (orbits) of height two nilpotent symmetric matrices have many pleasant
    properties, and give insights into the structure of interesting
    irreducible unitary representations of SL(n, R), the group of real n×n
    matrices of determinant one. If we replace SL(n, R) by a general reductive
    Lie group G, then its spherical nilpotent orbits have similar properties,
    and carry similar information about some of the irreducible unitary
    representations of G.
  • Clones in minors of matroids
    Carla Cotwright (Wake Forest University)
    Results that relate clones in a matroid to minors of that matroid are given. Also,
    matroids that contain few clonal-classes are characterized. These results are
    related to several results from the literature such as Tutte's Excluded-Minor
    characterization of the binary matroids.

    Joint work with T. James Reid.