August 8  17, 2007
Designing affordable, efficient, quiet supersonic passenger
aircraft has been under investigation for many years.
Obstacles to designing such aircraft are also many, both in
fundamental physics and in computational science and
engineering. The problem of design is multidisciplinary in its
nature and the goals of the constituent disciplines that govern
the behavior of an aircraft are often at odds. In particular,
aircraft that yields low sonic boom may not be attractive
aerodynamically, while aerodynamically optimized aircraft may
produce unacceptable sonic boom. One of the essential
difficulties in using direct optimization methods to design for
low boom and low drag is in modeling the design problem. For
instance, it is not clear what objective functions to use.
Some Early Boom Shaping
Developments (Ferri, 1969)
This project will use simple aerodynamic and sonic boom models
to examine modeling of the design problem itself. We will
attempt to establish a meaningful direct functional dependence
between the shape of the aircraft and aerodynamic and noise
quantities of interest by studying the sensitivity of these
quantities to changes in shape. We will experiment with several
direct multiobjective optimization problem formulations.
References:
 Seebass, R., Argrow, B.; "Sonic Boom Minimization
Revisited", AIAA Paper 982956

Shepherd, K.P., Sullivan, B.M.; "A Loudness Calculation
Procedure Applied to Shaped Sonic Booms", NASA Technical Paper
3134, 1991

Carlson, H.W., Maglieri, D.J.; "Review of Sonic Boom
Generation Theory and Prediction Methods", J. Acoust. Soc.
Amer., 51, pp. 675685 (1972)
 Alonso, J.J., Kroo, I.M., Jameson, A. "Advanced Algorithms
for Design and Optimization of Quiet Supersonic Platform", 40th
AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper
20020144, Reno, NV, January 2002
 Raymer, D.P.; "Aircraft Design: a Conceptual Approach",
Third Edition, AIAA, 1999
Prerequisites:
Required: Scientific computing skills (Matlab or
Fortran 90/95
or C), 1 semester in nonlinear optimization
Desired: Some background in statistical modeling,
numerical
analysis, multiobjective optimization
Keywords: multidisciplinary optimization, supersonic
design,
low boom, aerodynamic optimization
802.11 Wireless Local Area Networks (WLANs) have become as
ubiquitous as Internet access for personal computers. The basic
unit of a WLAN is composed of one Access Point (AP), and
several mobile stations (STAs), all forming a Basic Service Set
(BSS). A typical WLAN setup is depicted in Figure 1.
Figure 1: A typical Basic Service Set (BSS), with one AP, and
several mobile stations.
The IEEE Standard governing WLANs describes two modes of
operation: Distributed Coordination Function (DCF), and Point
Coordination Function (PCF). By and large, chipset
manufacturers implement only the DCF mode, and compatibility
testing is done for this mode exclusively. The DCF is a
contentionbased mechanism where each wireless device (AP, or
STA) competes for air time. More specifically, the 802.11
standard is implemented as follows:

At regular intervals (typically hundreds of ms) the AP
broadcasts a beacon signal, which resets all devices internal
clocks;
 Assume a transmission opportunity ended at time t0.
Depending on the status of the internal Backoff counter (BCK)
of the device, the following actions can take place:
 If BCKr=0, and there is no activity on air for DIFS
(Distributed Inter Frame Spacing = 50us in 802.11b) time, then
station starts transmitting its data packet;
 If BCK=0 and during the DIFS period there is activity
on air then device generates a random BCK between 0 and CW1
(initially CW=CWmin = 16, in 802.11b); Then the following rules
apply:
 For each slot time (Ts) of medium inactivity, the BCK
decrements;
 The countdown is stopped whenever medium is busy, and
the the countdown is resumed only after a supplemental AIFS
(Arbitration Inter Frame Spacing, =DIFS in 802.11b) wait;
 When BCK reaches 0, the device transmits its packet
data;
 If receiver (AP, or STA) receives successfully the
packet, then it sends back on the air an Acknowledgement (ACK)
frame, after a SIFT (Short Inter Frame Spacing = 10us) period
after transmitter finishes its transmission;

If transmitter receives the ACK correctly, then it
assumes data was received correctly, and transmission ends; On
the other hand, if ACK is not broadcast, or the transmitter
does not receive correctly the ACK, then it assumes the
transmission was not successful, and the following rules apply:
 If current number of retransmissions has not reached a
max threshold, then increment the Number of Retransmissions
counter
 If CW
Project description:
Astronomical telescopes detect the passage of an earthorbiting
object as a streak in an image. Over a period of months, it is
possible that many objects will pass through the field of view,
some appearing more than once. There are estimates of 100,000
objects in orbit that might be detected by high resolution
telescopes. A large field of view telescope may see 100
streaks a night. Most of these objects are space debris that
pose a hazard to operational satellites. There is keen interest
within the space community to discover and track all these
objects.
If the telescope sensor is properly instrumented, it is
possible to obtain timetagged pairs of angles that relate the
space object position to the sensor. With enough angle pairs,
it is possible to estimate the position and velocity (the
state) of the object, along with estimates of the uncertainties
of these parameters. The workshop problem is to develop
techniques to identify all the streaks made by each object.
Streaks created by an object must somehow be associated with
one another and disassociated from those made by other objects.
One solution approach treats the state data as vectors in R6
and uses statistical clustering techniques for the association.
A variation on this approach addresses physical properties of
the orbits, sorting according to those least likely to change
with small state variations.
Regardless of the approach, there are several interesting
aspects to the problem. Automatic streak detection is
required, with transform techniques of interest. Orbit
mechanics are essential to effective state estimation as well
as clustering techniques. In addition, traditional clustering
techniques are computationally taxing. A related problem is
identification of asteroids that might pose a hazard to planet
earth.
References:
Vallado, David A., Fundamentals of Astrodynamics
and Applications, Edition 2, Microsoft Press, 2004; Milani,
Andrea, "Three Short Lectures on Identifications and Orbit
Determination,"
http://copernico.dm.unipi.it/~milani/preprints/preprint.html,
2006; Kaufman, L. and Rousseeuw, P., Finding Groups in Data 
An Introduction to Cluster Analysis. Wiley Interscience 2005
Prerequisites:
Required:
computing proficiency demonstrated by knowledge of at least one
compiler, one semester differential equations, one semester
statistics
Desired: one
semester numerical analysis, familiarity with orbit mechanics
and estimation theory.
Keywords: orbit mechanics, astronomical telescopes,
statistical clustering
The Panstarrs telescope on Mount Haleakela in Hawaii will be
used, among other tasks, to search for asteroids. However,
using its 1.4 billion pixel sensor, it will also detect
earthorbiting objects.
Presently, when a physics motivated vehicle designer explores
vehicle
designs for a new concept, he is often faced with an enormous
range of
choices and constraints. For an example, an aircraft designer
has
Aircraft shape, fuel type, and engine as his main free
variables. While
his main constraints are dictated by the laws of physics
(weight, size,
power, lift, and stall). Additionally, he has his objective
which is
typically some combination/subset of acceleration,
maneuverability,
range, endurance, payload capacity (size, weight and power),
max and min
speeds, manufacturing cost, maintainability, reliability,
development
cost, takeoff length, landing length, noise footprint and other
items.
I am interested in examining the following problem: Given a
set of
performance objectives, how does one determine the space of
designs
available to the designer and find the optimal designs? How
does the
designer best visualize this space of options? Because he
doesn't want
just "the" answer, he wants to understand many aspects of the
answer.
While I'm interested in the general vehicle design problem, we
will
focus on aircraft design using a baseline tool that is to be
determined
as a concrete example with which we can test our ideas.
Traditional noninvasive sensing technologies have generated information about only one or two dimensional projections of objects of interest. But the use of arrays of sensor components, and opportunities to rapidly move such arrays around objects of interest are enabling the practical generation of many forms of threedimensional data. For example, in acoustics there has been steady progression from onedimensional echo trains, to twodimensional acoustic images, to modern threedimensional reconstructions, on scales from ultrasound wavelengths to global seismic surveys. Similarly, threedimensional tomographic reconstructions from xrays are now commonly used to resolve ambiguities in traditional twodimensional xray images.
As more threedimensional data becomes available, the value of automatic tools for utilizing such data increases. Several desired applications need methods by which to automate the finding of correspondences between threedimensional data sets. These threedimensional data sets frequently share many geometric characteristics, but also have significant differences, due to differences in data collection geometries, changes in sensor capabilities, temporal changes in the object of interest, and noise in the data.
One approach to finding unknown coordinate transformations, which are needed to align multidimensional data sets, is to require an expert to examine each set and label certain common landmarks. If sufficient landmarks, having the same unique labels can be found in both sets, the threedimensional coordinates of the landmarks enable the coordinate transformation to be estimated. This is like aligning images of faces, by first extracting the coordinates the tips of the noses, the left corners of the mouths, the bases of the right earlobes, etc.
But when no prior expertise is available, we need methods of estimating the transformation from set of automatically generated coordinates of 'interesting' locations (unlabeled landmarks). We expect that a significant subset of corresponding unlabeled landmarks may exist somewhere in the data set to which we need to compare. To solve our alignment problems, we need to devise automated methods to robustly find a pair of large subsets from a pair of sets of unlabeled landmarks, such that the subsets have similar geometric characteristics.
Does there exist a rigid motion mapping the
configuration of red points onto a subset of the blue points?
If so, what is the blue subset, and what is the rigid motion?
If not, how much deformation of the red configuration is needed
to make it so?
In principle, these problems can be solved by exhaustively comparing every possibility, but the level of effort grows exponentially fast with the number of landmarks. Our goal will be to find and test new approaches to this problem, seeking to devise algorithms which are robust and far more efficient.
References:
 Oliver Faugeraus, ThreeDimensional Computer
Vision, MIT Press, 2001
 Ian L. Dyrden, Kanti V. Mardia, {Statistical Shape Analysis}, Wiley, 1998
 D. G. Kendall, D. Barden, T. K. Carne, H. Le, Shape and
Shape Theory, Wiley Series in Probability and Statistics, 1999
 Gene H. Golub, Charles Van Loan, Matrix
Computations, Johns Hopkins University Press, 1996
Prerequisites:
Basics of linear algebra and matrix theory, basic computer programming skills, elementary Euclidean geometry
Desired: Ability to bring relevant ideas from one or more of geometry, invariant theory, optimization theory, graph theory, combinatorics, or something else.
Today's optical telecommunication networks carry audio, video
and data
traffic over fiber optics at extremely high bit rates. The
design of
such networks encompasses a range of challenging combinatorial
optimization problems. Typically, these problems are
computationally
hard even for restricted special cases. In this project we
study how to
assign wavelengths and place equipment so as to carry a set of
traffic
demands in large scale optical networks.
Our design problems are motivated by a popular optical
technology called
Wavelength Division Multiplexing (WDM). In this setting each
fiber is
partitioned into a fixed number of wavelengths and demands
sharing a
common fiber must be transported on distinct wavelengths. A
demand
stays on the same wavelength along its routing path as much as
possible.
When this is infeasible, we can either deploy an extra fiber
for the
demand to continue on the same wavelength; or place a
wavelength
converter for the demand to continue on a different wavelength.
Both
options incur cost. One objective is to assign wavelengths and
place
converters in an advantageous way so as to minimize the total
cost.
In this project we explore algorithms and heuristics for
assigning
wavelengths and placing converters. The goals include studying
the
tradeoff between optimality and complexity and understanding
the gap
between theoretical bounds and practical performance.
References:
[1] Matthew Andrews and Lisa Zhang, Complexity of Wavelength
Assignment
in Optical Network Optimization. (Please see Section VI.)
Proceedings of
IEEE INFOCOM 2006. Barcelona, Spain, April 2006.
http://cm.belllabs.com/~ylz/2006.coloring4.pdf
[2] C. Chekuri, et al. Design Tools for Transparent Optical
Networks.
Bell Labs Technical Journal. Vol. 11, No. 2, pp. 129143,
2006.
Prerequisite:
Required: One semester of algorithms; One semester of theory of
computing; One semester of programming.
Desired: Knowledge of Python and CPLEX.
Keywords: Analysis of algorithms, combinatorial optimization,
implementation of heuristics