[2018 Fall Semester]
매주 화요일 12:00
운영위원 : 장현태 ( a24325@ajou.ac.kr , 팔달관 622호 )
감독위원 : 문지연 ( j9746@ajou.ac.kr , 팔달관 622호 )
Title : Classification of lattice polygons with 3 interior lattice points
Abstract : lattice polygon is a convex polygon which has lattice points as vertices. Integral unimodular transformation is a translation follows area preserving linear transformation such that the entries of the matrix corresponding linear transformation are integers. Two lattice polygons are said to be equivalent if there is an integral unimodular transformation from 1 to the other. Rabinowitz classified all lattice polygon with at most one interior lattice points up to equivalence. Later, Wei and Ding proved that there are only 45 lattice polygons having two interior lattice points up to equivalence. Based on these results, I classify all lattice polygons with 3 interior lattice points up to equivalnce.
Title : Study on toric topology
Abstract : For a simplicial complex and a characteristic map over it, one can define a topological space called the real toric space. Using a piecewise linear sphere simplicial complex to construct it, a smooth manifold is obtained. We introduce several theories about the toric space.
Title : Sinkhole detection from GPR data using deep learning
Abstract : GPR(Ground Penetrating Radar) is one of the underground exploration methods to detect subterranean matter by detecting micro-electromagnetic waves that are reflected by radar. Raw data from GPR-machine can be verified as image from various software that can read GPR. If there is something under the ground, which affects the electromagnetic wave, it can be seen that the image shows different shape from the surrounding. The disadvantage is that you can not know exactly what kind of burial there is at that location. It is possible to distinguish the type of buried underground by deep-learning, and then we do not have to dig the ground. Among other things, we want to look for sink holes from raw data that are potentially dangerous in the downtown area.
Title : On the Erdos-Moser problem
Abstract : Erdős–Moser conjecture (1965) is about the sum of elements of a set of real numbers: For a given odd integer $n=2m+1$, $|T\subsetS : t\in T, \Sigma t =\alpha |$ for set $S$ of $n$ real values, is maximized when $S=\{-m, -m+1, \ldots, 0, 1, \ldots, m \}$ and $\alpha=0$ .
In 1980, R. Stanley used the Hard Lefschetz theorem to prove the (k-)Sperner property of the poset $G/P$ for $G$ a Weyl group and $P$ a maximal parabolic subgroup of $G$, which gave proofs of Erdős–Moser conjecture and some variations of it.
We consider more variations of the Erdős–Moser problem and provide answers to them.
Title : An introduction to symbolic dynamics
Abstract : Symbolic dynamics is the study of shift spaces. It is related to ergodic theory, automata theory, and information theory. In this talk, we introduce some classes of shift spaces, entropy of a shift space, and how to calculate entropies of some classes of shift spaces.
Title : On the cases of pareto and related distributions.
Abstract : There are some data sets can not be described in the normal distribution. For instance, there are some data sets have a thick tail compared with other distributions. That is, they have higher probability near their tails with respect to probability density function. If we use the normal distribution to describe these data sets, it can make serious errors. We use the fat-tailed distribution which can explain these appearances and study the pareto distribution, the fat-tailed distributions, generally used in a social science.
We check if the pareto distribution could describe the size of human settlements well known as approximately pareto-distributed. and decide whether the pareto distribution is appropriate to describe these data sets of relatively small size descent. In addition, we analyse the size of traffic jam in a big city by using various distribution functions.
Title : Estimation of seasonal correction factors for indoor radon concentrations in Korea.
Abstract : Long-term exposure to high radon concentration exerts pathological effects and elicits changes in respiratory function, increasing an individual’s risk developing lung cancer. In health risk assessment of indoor radon, consideration of long-term exposure thereto is necessary to identify a relationship between indoor radon exposure and lung cancer. However, measuring long-term indoor radon concentration can be difficult, and a statistical model for predicting mean annual indoor radon concentrations may be readily applicable. We investigated the predictability of mean annual radon concentrations using national data on indoor radon concentrations throughout the spring, summer, fall, and winter seasons in Korea. Indoor radon concentrations in Korea were highest in the winter and lowest in the summer. We derived seasonal correction and seasonal adjustment factors for each season based on the method proposed by Pinel et al. (1995). However, these factors may not be readily applicable unless measured in a specific season. In this study, we separate seasonal correction factors for each month of the year (new correction factors) based on correlations between indoor radon and meteorological factors according to housing type. To evaluate the correction factors, we assessed differences between estimated and measured mean annual radon concentrations. Roughly 97% of the estimated values were within $\pm40 Bq/m^3$ of actual measured values in detached houses, and roughly 85-87% of the estimated values were within $\pm40 Bq/m^3$ of the measured values in other residences.