AMSC 663-664 Projects, 2006-2007
Below are the links to each student's AMSC 663-664 project webpage.
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Qiwen Chen
(qchen "at" math.umd.edu)
Project Title:
Implementing CDO Models
Project Supervisors:
Dilip Madan
(Finance, dmadan "at" rhsmith.umd.edu)
and M. Fu (Decision & Information Technologies)
Abstract: A Credit Default Swap is a contract in which party A pays B a
regular cash flow till maturity in exchange for a compensation
payment from party B in an event of default of the underlying
corporate bond.The cash flow as a percentage of the notional,
aka credit spread, is determined in such a way that the
contract is worth 0 at initiation of the contract.The cash flow
reflects the probability of the event of default that two
parties agreed upon. A CDO is a pool of CDSs, of which the
cumulative loss on the pool is devided into different
tranches. A tranche holder receives regular cash flow as a
percentage of the remaining balance of that tranche and pays
out as loss occurs for which that tranche is responsible till
maturity.For example, the holder of the 3%-7% tranche gets
quarterly cashflow as a percentage of the balance. When the
total loss of the pool exceeds 3%, the balance of 3%-7% starts
to reduce. When the total loss reaches 7%, the balance of that
tranche is gone. The cashflows of all the tranches are
determined as the same way as CDS and they reflect the JOINT
distribution of the default events of all the underlying CDS
contracts. As the standardized CDO index, such as CDX and
iTraxx, came to trade in public,people are more interested in
capturing risk-neutral information regarding credit correlation
among companies, which made possible the creation of bespoke
CDO.
Project Propose:
(document,
slides)
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Christopher S. Groer
(cgroer "at" comcast.net)
Project Title:
Large Scale Vehicle Routing Problems
Project Supervisors:
Bruce Golden
(Decision & Information Technologies, bgolden "at" rhsmith.umd.edu)
Abstract: In this project, we propose to study and
implement several recently proposed algorithms for very large
scale Vehicle Routing Problems, a combinatorial optimization
problem that is a generalization of the better known Traveling
Salesman Problem. We will implement several of these
heuristic algorithms by creating an efficient C++ library that
will implement all of the commonly used primitive route
operations and improvement methods. We will then compare the
performance of these algorithms on different types of problems
in hopes of gaining deeper insight into these heuristics.
Time permitting, we will explore the development of new hybrid
heuristics and parallelization
Project Propose:
(document,
slides)
Reference
End of Fall Semester Report:
(document,
slides)
-
Malina A. Kirn
(m.a.kirn "at" gmail.com)
Project Title:
Fast pattern recognition for CMS track finding
Project Supervisors:
Nick Hadley
(Physics, hadley "at" physics.umd.edu)
Abstract: The primary goal of the project is to improve
the running time of an existing track finding algorithm
designed for the CMS experiment. CMS is an experiment
currently being built at the Large Hadron Collider (LHC), the
newest particle accelerator, also under construction. The
tracker is a component of the CMS detector and is used to
reconstruct the tracks of charged particles originating from
the collision point of the LHC proton-proton beams. There are
two track finding algorithms currently under development and
track finding currently consumes ~50% of CMS event
reconstruction computing time; so slow that event
reconstruction would take the next several decades for a
reasonable sized dataset. I plan to improve the running time
of one of these track finding algorithms in a quantifiable,
documented manner. This improvement may take the form of
numerous small improvements to existing code or the
replacement of current modules with faster, more
sophisticated algorithms performing the same task.
Project Propose:
(document,
slides)
Project Blog
End of Fall Semester Report:
(document,
slides,
Appendix)
-
Tamara Singleton
(tsingl "at" math.umd.edu)
Project Title:
Studying Ensemble Forecasting and the Breeding Method using a 1-D
and 2-D Cirrus Cloud Model
Project Supervisors:
Eugenia Kalnay
(Atmospheric and Oceanic Science, ekalnay "at" atmos.umd.edu)
and
David O'Starr
(NASA/GSFC, starr "at" agnes.gsfc.nasa.gov)
Abstract: The atmosphere is a chaotic dynamical system
composed of many layers defined by temperature
gradients. Numerical models were developed for studying the
dynamics of the atmosphere. Specifically, an atmospheric model
is an initial-value problem used to make forecasts and
predictions on the behavoir of the atmosphere. Because of the
unpredictable nature of the atmosphere if there is a small
error in the initial condition, we will be led to growing
errors in the forecast which will affect our prediction
capabilities.
Ensemble forecasting has been adapted to improve
computer-based forecasting and predictions by highlighting the
forecasting system's deficiences. Lorenz (1965) showed that
ensemble forecasts are more accurate than the individual
forecasts. The breeding method is used to generature
perturbations for ensemble forecasts. This study will use
ensemble forecasting and the breeding method to find the
dominant instability in the evolution of the solutin in a
one-dimensional and two-dimensional cirrus cloud model.
Project Propose:
(document,
slides)
End of Fall Semester Report:
(document,
slides)
-
M. Aaron Skinner
(aaronskinner79 "at" gmail.com)
Project Title:
The Athena MHD Code in Curvilinear Geometries
Project Supervisors:
Eve Ostriker
(Astronomy)
Abstract: The Athena code by Stone and Gardiner is a new,
second-order Godunov-type code for solving the equations of
ideal magnetohydrodynamics (MHD). One of its most salient
features is that it an unsplit method, making it a fully
conservative. This differs from other MHD codes such as Zeus,
the predecessor to Athena, in that it fully preserves the
divergence-free constraint, $\deldot \vb = 0$, to within
machine round-off error. Athena accomplishes this with a
hybrid combination of the Constrained Transport (CT) and
Corner Transport Upwind (CTU) methods. The equations of ideal
MHD consist of 8 coupled partial differential equations,
which are generally not solvable analytically. In full
Cartesian 3-D, numerical solutions can be quite
costly. However, many astrophysical systems of interest such
as accretion disks and protostars can be simplified by
exploiting curvilinear symmetry. For example, in accretion
disks, the high angular velocity of the plasma allows one to
consider properties such as net velocity to be constant
within a given annulus, that is, as a function of radius
only. Often, exploiting symmetry in this way can reduce the
effective dimension of the problem, which can greatly
simplify the calculations involved and allow finer resolution
when needed. The goal of this project is to adapt the
existing 2-D Athena code to include curvilinear geometries. I
will do this in a general way that will allow both
cylindrical and spherical polar coordinates to be included at
once. In each case, the ignorable coordinate will be
$\phi$. This will involve a reformulation of the MHD
equations so that the finite-difference algorithm is altered
as little as possible.
Project Propose:
(document,
slides)
-
Kareem A. Sorathia
(k.prophet "at" gmail.com)
Project Title:
Incorporating Radiative Transfer into Athena
Project Supervisors:
Chris Reynolds
(Astronomy, chris "at" astro.umd.edu)
Abstract: In the past 15 years accretion disk theory has
undergone a revolution caused by the discovery that the
principal mechanism of angular momentum transport is mediated
by MHD turbulence and driven by the magnetorotational
instability. Due to this new understanding of the underlying
physics of accretion disks as well as the continuing increase
of computational power, it is now possible to construct
first-principles MHD simulations of accreting disks of weakly
magne- tized plasma. However, pure MHD calculations are not
sufficient to adequately describe the physics involved in the
most luminous types of accretion disk sys- tems, such as
quasars and galactic black hole candidates. The large amount
of electromagnetic radiation emitted by these types of
systems make it necessary to incorporate the emission and
absorption of radiation into the dynamics of the accretion
flow.
The goal of this pro ject is to make a first step towards
including the physics of radiative transfer into an already
established MHD code. The MHD code to be used is Athena, a
newly released total-energy, ideal MHD Godunov code, created
by Jim Stone and based on its predecessor Zeus [2]. A full
treatment of radiation hydrodynamics (RHD) and radiation
magnetohydrodynamics (RMHD) will not be implemented. We will
assume the flux limited diffusion (FLD) approximation as well
as assume that the matter and radiation will be coupled only
through emission and absorption. These approximations will be
valid in the study of gas-pressure dominated thin accretion
disks. The scientific goals of this pro ject will be to
examine the dynamics and thermodynamics of such disks, as
well as the magnetic heating of the low density coronae on
disks.
Project Propose:
(document,
slides)
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