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Speaker: Ron Fox, Physics, Georgia Tech

Title: Rectified Brownian motion in cell biology

Abstract: At the nanometer lengthscale, thermal motion becomes very robust and significant. Inside living cells many protein function mechanisms benefit from this highly energetic form of energy. Quantitative analysis reveals a number of surprises. These will be exhibited for the quinone electron shuttle, rotary enzymes and the motor protein kinesin. In the last case, a mean first passage time analysis will be described that explains why these motors stall when loaded by more than a 6 piconewton force.

Speaker: Bob Foley, ISyE, Georgia Tech

Title: TBA

Abstract:

Speaker: Yichuan Zhao, Department of Mathematics and Statistics, Georgia State University

Title: Empirical Likelihood Based Confidence Bands for Survival Functions and Ratios of Survival Functions

Abstract: We derive a simultaneous confidence band for the ratio of two survival functions based on independent right-censored data. Earlier authors have studied such bands for the difference of two survival functions, but the ratio provides a more appropriate comparison in some applications, e.g., in comparing two treatments in biomedical settings. Our approach is formulated in terms of empirical likelihood and allows us to avoid the use of simulation techniques that are often needed for Wald-type confidence bands.

A popular simultaneous confidence band for survival functions is the equal precision band of Nair (1984). This band is found by adjusting the level of Wald-type pointwise confidence intervals centered on the Kaplan--Meier estimator. We develop a complementary method of adjusting pointwise confidence intervals to produce a simultaneous band. Our approach is to scale the width, rather than the level, of the pointwise confidence intervals. The resulting adjustment of the pointwise band, called a width-scaled band, provides an attractive alternative to the equal precision band. Empirical likelihood and Wald-type versions of width-scaled bands are derived in one- and two-sample censored data settings.

Our approach is illustrated with a real data example.

Speaker: Dave Goldsman, ISyE, Georgia Tech

Title: To Batch Or Not To Batch

Abstract: When designing steady-state computer simulation experiments, one is often faced with the choice of batching observations in one long run or replicating a number of smaller runs. Both methods are potentially useful in the course of undertaking simulation output analysis. In its simplest form, the choice boils down to: Should we divide one long run into b adjacent, nonoverlapping batches, each of size m? Or should we conduct b independent replications, each of length m? The trade-offs between the two alternatives are well known: Batching ameliorates the effects of initialization bias, but produces batch means that typically are correlated; replication gives independent sample means, but may suffer from initialization bias at the beginning of each of the runs.

In this talk, we give several new results and specific examples to lend insight as to when one method might be preferred over the other. We find that, in the steady-state case, batching and replication perform about the same in terms of estimating the mean and variance parameter. However, in the steady-state case, replication tends to do better than batching when it comes to the performance of confidence intervals for the mean. On the other hand, batching can often do quite bit better than replication when it comes to point and confidence-interval estimation of the steady-state mean in the presence of an initial transient. (Joint work with Christos Alexopoulos, ISyE)

Speaker: Frank Dellaert, College of Computing, Georgia Tech

Title: Markov Chain Monte Carlo in Vision & Robotics Applications

Abstract: In this talk I will give an overview of my work in using MCMC sampling in computer vision and robotics problems. I will give a short introduction to the 3D structure recovery problem in vision, and where MCMC sampling comes in to solve the long-standing correspondence problem. In particular, I show that this problem can be formulated in an Monte Carlo EM framework, where MCMC sampling over bipartite matchings is used to implement the E step. The resulting method enables the recovery of 3D structure from unlabeled, 2D measurements in a set of images. In the second half of the talk, I will talk about current directions that my students and I are exploring, in particular building probabilistic topological maps for robotics, recovering semantics in architectural scenes, and sampling over piecewise continuous 3D curves to model pot shards for archeological applications.

Speaker: Susmita Datta, Department of Mathematics and Statistics, Georgia State University

Title: Some statistical issues in the analysis of microarray data

Abstract: One of the most active areas of Bioinformatics research today is the analysis of microarray data. Modern microarray technology has enabled biologists to record the expression profiles of thousands of genes in a single experiment. The large volume of data generated from these experiments (many available on public internet sites) has created tremendous opportunities for the statisticians to get involved in this exciting development and create appropriate statistical tools for analyzing these data. In this talk, we will address two statistical problems in this area. The first deals with the selection of a good clustering algorithm for a given data set and the second deals with the issue of multiple testing in detecting the differentially expressed genes out of a list of over ten thousand genes.

Speaker: David McDonald, University of Ottawa

Title: Mean-field convergence of distributed dynamical systems sharing a common resource

Abstract: Multiple TCP/IP connections multiplexed through a RED buffer are in fact dynamical systems which share a common resource - the buffer. We adapt the technique developed by Kurtz and Donnelly to prove mean-field convergence of the histogram of window sizes.

Speaker: Marco Dall'Aglio, University of Pescara

Title: Nonlinear partitioning problems

Abstract: We consider the classical problem of dividing an object among n participants so that everybody is satisfied with the part received. In the literature, it is almost always assumed that the utilities of the agents are linear (i.e. marginally constant), monotonic and continuous, and, consequently, they are represented by continuous (atomless) probability measures on the object to be divided. Hill (1987) removes continuity by allowing measures to have atoms of a given size, while Berliant, Dunz and Thomson (1992) and Maccheroni and Marinacci (2002) offer a first attempt to consider concave (i.e. marginally decreasing) utilities. Our aim is to weaken the monotonicity and continuity assumptions, while keeping concavity. This setting seems particularly suitable in the context of land division, where free disposal of land is usually not allowed (joint work with Fabio Maccheroni).

Speaker: Liang Peng, Schoool of Mathematics, Georgia Tech

Title: Garch models and nonparametric regression with infinite variance

Abstract: The class of GARCH models is arguably the most frequently used family in modeling conditional second moments. For parameter inference the conventional quasi-maximum likelihood estimator suffers from complex limit distributiuons and slow convergence rates in some cases. In the first part of this talk, we study the least absolute deviations estimators and show that the one based on logarithmic transformation is asymptotically normal. Further we apply this estimator to estimating the tail index of the error distribution, which may be an important guide to incorporate heavy tailed errors into GARCH models. In the second part of this talk, we consider local least absolute deviations estimator for trend functions of times series with heavy tails which are characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable ARIMA model as special cases. The asymptotic normlity of this estimator is established under the assumption that the process has either short or long range dependence.

Speaker: Carl Spruill, School of Mathematics, Georgia Tech

Title: Convergence Rates for Renewal Sequences with Applications

Abstract: The methods of renewal sequences can be applied to restarted simulated annealing, for example, to show that the probability p_n the goal has not yet been attained by the n^th iteration converges to zero geometrically fast and to characterize the precise rate of this convergence. Other applications include counters, success runs, and queueing.

Fall 2002

CDSNS Colloquium | CDSNS/ACELab | Colloquium | Combinatorics | Geometry | Geometry/Topology/Algebra | Nonlinear Science | Research Horizons | Stochastics | Topology |