November 3 - 4, 2006
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.
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.
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.
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.
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.
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.
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/
In collaboration with Guerrero et al from MD Anderson Cancer Center,
we are developing a new method for accurate registration of 4D CT lung
images which accounts for: (1) the compressible nature of the lungs,
(2) noise in the images, (3) the high computational workload required to
register 4D CT image sets.
In order to account for lung compressibility, voxel displacement is modeled
by the conservation of mass equation. Secondly, the
effects of noise are alleviated by applying the local-global approach of
Weickert et al. to the conservation of mass setting. Finally, the resulting large scale linear
systems are solved using a parallelizable, preconditioned conjugate gradient algorithm.
The new method has been implemented in serial and tested on two dimensional
sythetic images with promising results.
Recurrent epidemics of influenza are observed seasonally around the world
with considerable health and economic consequences. Major changes in the
influenza virus composition through antigenic shifts can give rise to
pandemics. The reproduction number provides a measure of the
transmissibility of influenza. We estimated the reproduction number across
influenza seasons in the United States, France, and Australia for the last
3 decades. In regards to pandemic influenza, we estimated the reproduction
number for the first two epidemic waves during the 1918 influenza pandemic
in Geneva, Switzerland. I will discuss the public health implications of
our findings in terms of controlling regular influenza epidemics and an
influenza pandemic of comparable magnitude to that of 1918.
For Hunt processes with jumps, we seek a treatment that concentrates
on the jumps. The idea is to use a generalized version of the renewal
theory (to which Blackwell was a seminal contributor). Embedded at
the jump times, there are Markov renewal processes (with continuous
state space) that decompose the original process into a sequence of
diffusions. Then, the original resolvent can be written as the
potential operator of a Markov chain acting on the resolvent of a
diffusion. Similar decompositions are possible for hitting
distributions and the transition semigroup. Theoretically, our
method reduces a jump diffusion to a combination of diffusions and
Markov chains.
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.
Biological systems often include very interesting
fluid flows that arise from the interaction of a
fluid with an external source of force. Examples
are the motion of micro-organisms, such as bacteria,
that propel themselves by moving their flagella, the
motion of cells, and the motion generated by cilia
beating in the lungs. The common theme is the
interaction between the fluid and an elastic membrane
of filament. Numerical models of these motions must
compute the motion of the membranes and the fluid
simultaneously. This talk highlights the use of
Regularizaton Methods for these problems, a methodology
that has shown promising results and that continues
to expand. Examples of the computations will be shown.
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.
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.
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.
The transport of wide variety of phenomena in turbulent flows (heat,
mass, momentum, species, etc.) is a significant challenge to
computational scientists and engineers working in chemical
processing, pharmaceuticals, materials synthesis, and atmospheric
physics, to name a few. Capturing the variety of length and time
scales manifest in these flows leads to compute times which are
impractical at best and infeasible at worst. In this seminar, I will
present some ideas and recent work in the modeling of multi-scale
transport phenomena and the probabilistic and stochastic tools used
in their description.
Linear regression is one of the most widely used statistical techniques. However, there is
often a problem of missing response variables in practical applications. The expectation maximization (EM) algorithm is a general iterative algorithm for the analysis of missing data; but it relies on parametric assumptions that are usually not met. We present a nonparametric algorithm--the empirical likelihood (EL) algorithm for linear models with missing data. The EL algorithm's advantage is that it makes no assumptions regarding the form of the underlying distribution of the data. We construct confidence
intervals for the mean response in the presence of missing responses. We also discuss the power and efficiency of confidence intervals constructed when using the EL algorithm to replace missing responses.
Sometimes differential equations have an obvious symmetry which leads
to a natural guess for its solution. The Norwegian mathematician
Marius Sophus Lie (1842-1899) spent most of his career attempting
to generalize ideas of fellow Norwegian Niels Henrik Abel (1802-1829) from discrete groups of symmetries of algebraic objects to
continuous groups of symmetries of topological objects. In the
process, Lie created a new branch of mathematics which united
differential geometry and abstract algebra.
In this talk, we give a brief introduction to the pulchritude of
Lie's ideas. From the geometric nature of manifolds to the analytic
nature of differential equations, we discuss the natural group action
of the space of vector fields of a manifold on itself. We conclude
the talk with a discussion of the computation of Lie group of the
real line.
This talk gives a general overview of an emerging technique for discrete
optimization that has footholds in mathematics, computer science, and
operations research: branch decompositions. Branch decompositions along
with its respective connectivity invariant, branchwidth, were first
introduced to aid in proving the Graph Minors Theorem, a well known
conjecture (Wagner's conjecture) in graph theory. The algorithmic
importance of branch decompositions for solving NP-hard problems modeled
on graphs was first realized by computer scientists. The dynamic
programming techniques utilizing branch decompositions, called branch
decomposition based algorithms, fall into a class of algorithms known as
fixed-parameter tractable algorithms and this talk will highlight the
computational effectiveness of these algorithms in a practical setting
for NP-hard problems such as the travelling salesman problem, general
minor containment, and the branchwidth problem.
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.
Come learn about opportunities at SAMSI.
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.
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.
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.
Come learn about the exciting opportunities in the Computation Directorate
at LLNL.
In this talk we explain how a single jump non-stationary queueing control problem can be
solved via sensitive optimality criteria. In particular, the queueing problem is divided into a
stationary infinite horizon problem and a non-stationary finite horizon problem with the
appropriate terminal reward. The stationary problem leads to several results including the
existence of a single bias optimal policy. Since the existence of a Blackwell optimal policy
is known, this implies a similar result under this criterion. The search for an optimal policy in
the non-stationary problem is shown to lie within the class of monotone (in time) control limit
policies. The original problem was posed by Professor Massey and lead to an understanding of
an application of Blackwell's sensitive optimality criterion, thereby drawing a connection
between 2 (actually 3) generations of African-American scholars.
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.
Technological innovations are creating new types of communication systems such as call centers, electronic
commerce, and wireless communications. Communication services managers must make important business decisions
to stay competitive and profitable. They have to maximize the communication resources that they are making
available to the customer. However, managers must also minimize their costs for providing these resources,
which results in maximizing profits for their companies.
The mathematical field of queueing theory was successfully introduced in the first half of the 20th century
to model voice communication networks. It has traditionally provided managers with a useful set of decision
making formulas, algorithms and policies for designing communication systems and services.
Another major triumph for queueing theory happened in the second half of the 20th century when it
was applied to data communication systems and contributed to the design of the first prototype for the Internet.
Both types of voice and data queueing models made significant use of the steady state theory for continuous time
Markov chains.
Given the new types of communication systems and services available in the 21st century, it is no longer possible
to make many of the simplifying assumptions of classical queueing theory. One major theme of my research has been
to move away from the static steady state analysis of the past and develop a theory of queues that captures more
of the true dynamic behavior that is found in real communications operations. My talk will discuss the types of
mathematical tools needed to create a dynamical queueing theory.
This involves new types of perturbation analysis applied to the differential equations of the transition
probabilities for the underlying, time-inhomogeneous Markov chain, queueing model. Moreover, we also use the theory
of strong approximations to apply this asymptotic analysis directly to the random sample paths of these stochastic
processes. We can also relax these Markovian assumptions by using the theory of Poisson random measures.
Finally, we can establish fundamental limit theorems that approximate many of these random processes by dynamical
systems. From these results, we can then apply the dynamic optimization techniques of variational calculus and
classical mechanics to the efficient design of these queueing models.
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
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.
Come learn about opportunities at MSRI.
In this talk we shall present some results on the asymptotic
behavior of spectra of Schrodinger operators with continuous potential on
the Sierpinski gasket SG. In particular, using the extence of localized
eigenfunctions for the Laplacian on SG we show that the eigenvalues of
the Schrodinger opeartor break into clusters around certain eigenvalue of
the Laplacian. Moreover, we prove that the characteristic measure of
these clusters converges to a measure.
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.
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.
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.
We introduce an integrodifference equation model to study the
spatial spread of epidemics through populations with overlapping and non-
overlapping epidemiological generations. Our focus is on the existence
of travelling wave solutions and their minimum asymptotic speed of
propagation c*. We contrast the results here with similar work carried
out in the context of ecological invasions. We illustrate the theoretical
results numerically in the context of SI (susceptible-infected) and SIS
(susceptible-infected-susceptible) epidemic models.
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.
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.
In this talk we introduce an option pricing model with
delayed memory. The memory is introduced in the stock
dynamics, which is described by a stochastic
functional differential equation. The model has the
following key features:
1. Volatility depends on a (delayed) history, i.e.,
its value at time t is a deterministic functional of
the history of the stock from time t-L up to time t-l,
where l is positive and less than or equal to L.
Hence, due to this past-dependence on the stock price,
the volatility is necessarily stochastic.
2. The randomness in the volatility is intrinsic,
since it is generated by past values of the stock
price.
3. The stock dynamics is driven by a single
one-dimensional Brownian motion, and the model is one
dimensional.
4. The market is complete.
5. For large delays (or at times relatively close to
maturity) we obtain a closed-form representation for
the fair price of the option, as well as for the
hedging strategy.
6. The option price can be expressed in terms of the
exact solution of a one-dimensional partial
differential equation (PDE).
7. The classical Black-scholes model is a particular
case of the delayed memory model.
8. We believe that our model is sufficiently flexible
to fit real market data, in particular to account for
observed "smiles" and "frowns".
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
mesocorticalmesolimbic pathway is the cause of (positivenegative)
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.
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
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.
Modern broadband communications requires antennas with greatly improved
frequency range and reduced size. It has been known since 1948 that
there are basic physical limitations on the bandwidth that can be
obtained for a given size antenna; however, the numerical results that
have been available were until recently based entirely on a second-order
model for the antenna that was (a) an approximation, and (b) only
strictly applicable to relatively narrowband cases. In the last few
years, a new approach based on "Fano's formulation" has been used which
can apply over any bandwidth. We have reformulated Fano's method as an
optimization problem and as a result have been able to obtain
fundamental bandwidth limits that can in principle be calculated for any
radiation mode. This means that one can now find the ultimate possible
bandwidth performance for directional antennas, a result with immediate
practical significance for designers of ultra-wideband antennas. Graphs
of numerical limits on the in-band reflection coefficient tolerance
versus electrical size for high-pass and band-pass tuning are presented.
This is joint work with H.D. Foltz and J.S. McLean
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.
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.
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 q^{m}-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.
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 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
The inhomogeneous higher-order nonlinear Schrödinger (IHONLS) equation is
studied by the use of generalized hyperbolic functions and the complex
amplitude method. The results reveal that for the new bright soliton-type
and dark soliton-type solutions obtained, one can control the velocity,
the phase shift (by managing the distributed parameters of the system) and
the shape (by choosing appropriately the two parameters introduced in the
generalized hyperbolic functions).