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Date
Wednesday
05.10.06
in room
08-2365
at Noon
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Amit Batabyal
RIT Arthur J. Gosnell Profess of Economics
The Infinitesimal, the Deterministic, and the Probabilistic: Alternate Container Inspection Policies in Invasive Species Management
Abstract:
Recently, Batabyal and Nijkamp (2005) have shown that in an inspection cycle, regardless of
whether the inspection policy choice is made on the basis of an optimization
exercise or on the basis of a rule of thumb, the ³container policy² dominates the ³temporal policy²
because the container policy results in lower long run expected net cost (LRENC) from inspections.
In this paper, we continue this line of inquiry and analyze container policies in three
scenarios. In the first scenario the time taken to conduct inspections is negligible. In the second scenario,
this inspection time is deterministic and in the third scenario this inspection time is stochastic.
Specifically, we compare and contrast the LREC and the optimal container policy in each of these three scenarios.
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Date
Wednesday
05.10.06
in room
08-2355
at 1 p.m.
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Gaurav Sharma
University of Rochester, Electrical and Computer Engineering Department
Multimedia Authentication Watermarks: Integrating Cryptography with Signal Processing
Abstract:
Digital representation and communication make information dissemination
easy in today¹s networked world. The ease of manipulation of the digital
data, however, also emphasizes the need for integrity verification. For
multi-media signals, often additional or different capabilities beyond
conventional cryptographic authentication are desirable. These needs are
addressed by authentication watermarks that not only provide the ability
to localize tampered signal regions, but also ensure immunity against
multimedia-specific attacks, which may be sometimes overlooked. In this
talk, we present our recent work in this area incorporating three main
ideas: a hierarchical image authentication watermark, a loss-less data
embedding technique, and a new framework for lossless authentication.
The hierarchical watermark allows authentication of integrity over a
pyramidal hierarchy, thus offering a trade-off between security and
localization under collage (vector quantization) attacks. The lossless
data embedding method provides a high-capacity low-distortion method for
watermark insertion that is reversible and allows recovery of original
image data --- a crucial requirement in some medical, legal and military
applications where integrity verification is important but common
watermarking distortion is unacceptable. The new lossless authentication
framework improves on existing lossless authentication watermarks by
allowing authentication of the image prior to recovery. This in turn
enables tamper localization which is often not realized in existing
methods. Finally, we present a lossless authentication watermark (LAW)
that implements the new framework by combining the hierarchical
authentication and the lossless embedding methods.
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Date
Friday
05.12.06
in room
08-2355
at Noon
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Anurag Agarwal
RIT Dept. of Mathematics & Statistics
Pursuit of Primes
Abstract:
In this talk we will explore through the journey of settling the question of
primality. Give a positive integer, how can we definitely and efficiently
test of it is a prime or composite? We will prensent some of the past and
modern day number-theoretic algorithms and the ideas that have led to the
complete answer to this question. In particular, we will also discuss the
ideas, facts and myths involved in the recently proved AKS algorithm about
primality.
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Friday,
05.05.06
in room
08-2355
at Noon
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Likin Simon-Romero
RIT Dept. Mathematics & Statistics
Introduction to Continuum Theory
Abstract:
In Topology, a continuum is a non-empty compact connected metric space.
In this talk, we will discuss some topological properties of continua
(like indecomposability and fixed point property) and we will give some
examples of continua that are related with such properties. We will
define the notion of hyperspace and show some models for hyperspaces of
different continua. Also, we will state some of the open questions in
Continuum Theory.
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Friday,
04.28.06
in room
08-2355
at Noon
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Wondimu Tekalign
RIT Dept. of Mathematics & Statistics
Modeling the Evolution of a dislocation-free thin solid films
Abstract:
We consider a continuum model for the evolution of an
epitaxially-strained dislocation-free thin solid film on a deformable
substrate in the absence of vapor deposition. By using a thin film
approximation we derived a nonlinear evolution equation. We examined
the nonlinear evolution equation and found that there is a critical
film thickness below which every film thickness is stable and a
critical wave number above which every film thickness is stable. We
developed a numerical method for the evolution of strained solid
films under the thin film approximation. The numerical method was
used to characterize the family of equilibrium shapes in terms of the
film thickness and the spatial periodicity for both two-dimensional
(island ridge) and three-dimensional (quantum dot) morphologies.
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Wednesday,
04.26.06
in room
08-2365
at Noon
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Peter E. Castro
Eastman Kodak
Random Acts of Industrial Mathematics
Abstract:
The large difference between academic and industrial mathematics will be
illustrated using several industrial applications intertwined through a mathematical thread of random processes.
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Wednesday,
04.21.06
in room
08-2355
at Noon
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Ephraim Agyingi
RIT Dept. of Mathematics and Statistics
A Mathematical Model of Epidermal Wound Healing in the Presence of an Infection
Abstract:
A robust mathematical model coupling capillary growth, oxygen supply,
macrophage-derived growth factors (MDGF), wound and bacteria densities, is
developed for the healing rate of an epidermal wound. The wound geometry is
circular and the model is based on diffusion equations. A one-dimensional
quantitative analysis is presented.
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Friday,
03.17.06
in room
08-2355
at Noon
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Kamlesh Parwani
University of Houston
Partially hyperbolic maps on 3-manifolds
Abstract:
Partially hyperbolic maps arise quite naturally in modeling
chaotic phenomenon such as weather--the famous Lorentz equations give
rise to partially hyperbolic phenomenon. We use the rich theory of
foliations to show that not all 3-manifolds can support partially
hyperbolic diffeomorphisms. In fact, if a 3-manifold supports a partially
hyperbolic map, its universal cover must be R3.
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Friday,
02.17.06
in room
08-2305
at Noon
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John R. Schott
Frederick and Anna B. Wiedman Professor
Head, Digital Imaging and Remote Sensing Laboratory
Chester F. Carlson Center for Imaging Science
Rochester Institute of Technology
Dimensionality-Curse or Solution: Algorithms for Imaging Spectroscopy
Abstract:
After reviewing aerial and space based remote sensing systems that generate spectral image data, the types of algorithms
used to analyze these spectral images will be introduced. This will include an introduction to spectral analysis in terms
of Matrix algebra and a review of classical spectral unmixing to address subpixel material characterization in spectroscopic
images. Two methods of spectroscopic image analysis that are evolving to address the subpixel target detection problem will
then be introduced. The first involves a statistical description of the target and the background clutter and the second uses
a subspace representation of the target and background clutter. Based on these introductory materials some of the ongoing
research at RIT on spectral image analysis will be summarized in the context of the conceptual approaches introduced. Most
importantly there are lots of aerial and satellite images to make math go down easily.
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Wednesday,
02.08.06
in room
08-1174
at Noon
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Dr. Lynn Wild
Rochester Institute of Technology
Groups That Work
Abstract:
Are your students working in groups or do they remain disjointed groups of
people? Although groups form a basic unit of work activity inside and
outside the classroom the underlying process is often poorly managed. This
brief session will examine best practices and pitfalls when creating and
working with groups. Some discussion topics will address the structure and
logistics of groups, such as:
- Preparing the Students
- Instructor's Tasks
- Classroom Environment
- Selecting Groups
- Types of Groups
- Group Dynamics
- Group Factors
- Why Groups Fail
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Friday,
02.03.06
in room
08-2305
at Noon
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Dr. Majid Rabbani
Eastman Kodak
The JPEG2000 wavelet-based still image compression standard
Abstract:
The joint ISO and ITU JPEG committee standardized a new still-image
compression standard in 2001, referred to as the JPEG-2000, which is
starting to appear in a diverse set of products. JPEG2000 is based on
wavelet compression and provides the potential for numerous advantages
over the existing JPEG standard. Performance gains include improved
compression efficiency at low bit rates or for large images, while new
functionalities include multi-resolution representation, scalability and
embedded bit stream architecture, lossy to lossless progression,
region-of-interest (ROI) coding, error resilience, idempotency to
multiple compression cycles, and a rich file format.
This presentation provides a brief overview of the various technical
components of JPEG2000 in addition to a software demonstration of some
of its capabilities.
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Friday,
01.13.06
in room
08-2305
at Noon
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Edieal Pinker
William E. Simon Graduate School of Business
University of Rochester
An analysis of Short-term Responses to Threats of Terrorism
Abstract:
Dr. Pinker will address the application of mathematics and probability to
understanding terrorism. Two important defensive mechanisms available to
governments combating terrorism are warnings and the deployment of physical
resources. Warnings are relatively inexpensive to issue but their
effectiveness suffers from false alarms. Physical deployments of trained
security personnel can directly thwart attacks but are expensive and need to
be targeted to specific locations. In this paper we model the joint
optimization of defenses against terrorist attacks based on warnings and
physical deployments when there is uncertainty in the timing and location of
attacks. We model both private warnings issued to security forces and
public warnings broadcast to the general public. By structuring the
tradeoffs faced by decision makers in a formal way we shed light on an
important public policy problem. We show that the interaction between the
use of warnings and physical defenses is complex and significant. For
public warnings we also model the possible response of terrorists and show
how these responses influence the effectiveness of such warnings.
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Friday,
12.09.05
in room
08-2305
at Noon
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Dick Doolittle
Rochester Institute of Technology
A New Approach to Teaching an Old Science: A Faculty Learning Community Pilot Project
Abstract:
This talk addresses how understanding human anatomy and physiology is of fundamental importance to student preparation for careers in medicine and the biomedical
sciences. In an attempt to improve the learning environment, a new model was implemented to promote active learning and to expand lines of
communication between students and faculty. Investment in student-led, faculty-guided classroom experiences that encourage cooperation and
collaboration will fit well with the characteristics of today's millennium students.
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Friday,
11.04.05
in room
08-2305
at 1:00 p.m.
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Dr. Nikos Apostolakis
City University of New York
Coloring knots
Abstract:
An introduction to the mathematical theory of knots (and links) will be provided followed by a discussion of the
fundamental problem of knot theory: Given two knots decide whether we can ``continuously
deform'' one into the other. Tri-colorings of
knots as a simple knot invariant will be introduced and the calculation
of this invariant for knots up to 10 crossings. How knot colorings
represent three-dimensional manifolds and how this relates to some of
my current research will also be discussed.
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Wednesday,
10.26.05
in room
08-1154
at 11:00 a.m.
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Dr. Allan Greenleaf
University of Rochester
The Radon Transform: Applications and Generalizations
Abstract:
The Radon Transform, which assigns to a function in the
plane the collection of all of its line integrals, was originally
introduced in 1917 to deal with a geometric problem of Funk. It was
rediscovered in the 1960's and became the mathematical basis for CAT
scans in medical imaging. In the meantime, it had also found
applications to partial differential equations and representation
theory. The study of generalized Radon transforms continues to be a
very active area of geometric analysis. This talk will give some of
the history, applications and extensions of the Radon transform.
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Friday,
10.21.05
in room
08-2305
at 1:00 p.m.
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Dr. Gahyun Park
Purdue University
Analysis of Biclusters with Applications to Gene Expression Data
Abstract:
For a given matrix of size n * m over a finite alphabet A, a
bicluster is a submatrix composed of selected columns and rows
satisfying a certain property. In microarrays analysis one searches for
largest biclusters in which selected rows constitute the same string
(pattern); in another formulation of the problem one tries to find a
maximally dense submatrix. In a conceptually similar problem,
namely the bipartite clique problem on graphs, one looks for the
largest binary submatrix with all "1." In this talk, we assume that the
original matrix is generated by a memoryless source over a finite alphabet
A. We first consider the case where the selected biclusters are square
submatrices and prove that with high probability (whp) the largest square
bicluster having the same row-pattern is of size [logQ (n m)]2 where
Q-1 is the largest probability of a symbol. We observe, however, that
when we consider any submatrices (not just square submatrices), then the
largest area of a bicluster jumps to A n (whp) where A is an
explicitly computable constant. These findings complete some recent
results concerning maximal biclusters and maximum balanced bicliques for
random bipartite graphs.
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Wednesday,
10.12.05
in room
08-1154
at 11:00 a.m.
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Dr. Daniel Stefankovic
University of Rochester
Crossing numbers of graphs
Abstract:
The crossing number of a graph is the minimum number of edge
intersections in a plane drawing of a graph, where each intersection
is counted separately. If instead we count the number of pairs of
edges that intersect an odd number of times, we obtain the odd
crossing number. Chojnacki (1934) and Tutte (1970) showed that
if the odd crossing number of a graph is zero then its crossing
number is zero. We will show that there is a graph for which these
two concepts differ, answering a well-known open question on
crossing numbers. To derive the result we study drawings of maps
(graphs with rotation systems). Joint work with Michael Pelsmajer
and Marcus Schaefer.
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