Abstract:
In this talk we will present our recent work on 3D LIDAR point clouds
compression. The new algorithm is based on the idea of compression by
classification. It utilizes the unique height function simplicity as well
as the local spatial coherence and linearity of the aerial LIDAR data and
can automatically compress the data to the desired level-of-details
defined by the user. The random sample consensus (RANSAC) and principal
component analysis (PCA) algorithms are employed for robust and efficient
local fitting and approximation. Moreover, supervised machine learning
techniques such as support vector machine (SVM) is used to automatically
detect regions that are not locally linear such as vegetations or trees.
In those regions, the local statistics descriptions such as mean,
variance, expectation, etc are stored to efficiently represent the region
and restore the geometry in the decompression phase. The new algorithm has
been tested in several aerial LIDAR datasets with very good results. If
time permits I will also discuss our recent work in virtual navigation of
the interior spaces of urban structures, rock geo-mechanics analysis for
highway safety, etc.

Let $C$ be a curve over a local field whose reduction is totally
degenerate. We discuss the related problems of 1) determining the
group structure of the torsion subgroup of the Jacobian of $C$, and 2)
determining if a given line bundle on $C$ is divisible by a given
integer $r$. Under certain hypotheses on the reduction of $C$, we
exhibit explicit algorithms for answering these two questions.

Advisor:  Professor Knut Solna

Advisor: Professor Knut Solna

Abstract: We introduce some popular models in the energy markets. Then we
propose to incorporate a stochastic volatility feature to an existing
multi-factor deterministic volatility model in order to take into account
the observed implied volatility skews for each of the commodities in the
simulation of monthly forward prices. As examples we consider natural gas,
crude oil and heating oil price and option data. Our objective is to
explore the role of stochastic volatility modeling for calibration and
simulation of price paths and scenario analysis. The linkage between
price, option data and modeling is captured by the so called "Vs" in our
approach. These are the effective group market parameters that capture the
main impact of an uncertain and fluctuating volatility, in particular how
these affect prices. To explore the significance of incorporating this
link we carry out an initial calibration test to explore the role of the
"Vs" in the commodity price distribution. We find that indeed the
distribution of the commodity prices are significantly affected by
incorporating the leading correction that accounts for the effect of
uncertain volatility parameters which manifests itself in the data via
strong "skew" effect in the option pricing data. An added benefit of this
modeling framework is that it enables us to use observations around and
not only at the money in a consistent way, thus, providing robustness and
stability in calibration also at the order one level.