|Annie (Peiyong) Qu, University of Illinois, Urbana-Champaign|
|Title: Time-varying networks estimation and dynamic model selection|
|Abstract: In many biomedical and social science studies, it is very important to identify and predict the dynamic changes of associations among network data over time. We propose a varying-coefficient model to incorporate time-varying network data, and impose a piecewise penalty function to capture local features of the network associations. The advantages of the proposed approach are that it is nonparametric and therefore flexible in modeling dynamic changes of association for network data problems, and capable of identifying the time regions when dynamic changes of associations occur. To achieve local sparsity of network estimation, we implement a group penalization strategy involving overlapping parameters among different groups. However, this imposes great challenges in the optimization process for handling large-dimensional network data observed at many time points. We develop a fast algorithm, based on the smoothing proximal gradient method, which is computationally efficient and accurate. We illustrate the proposed method through simulation studies and children’s attention deficit hyperactivity disorder fMRI data, and show that the proposed method and algorithm efficiently recover the dynamic network changes over time. The proposed approach works especially well when networks are sparse. This is joint work with Xinxin Shu.|
|(Tony) Jianguo Sun, University of Missouri, Columbia MO|
|Title: Regression Analysis of Longitudinal Data with Informative Observation Times and Application to Medical Cost Data|
Abstract: The analysis of longitudinal data with informative observation processes
has recently attracted a great deal of attention and some methods have been developed.
However, most of those methods treat the observation process as a recurrent event
process, which assumes that one observation can immediately follow another.
Sometimes, this is not the case, as there may be some delay or observation duration.
Such a process is often referred to as a recurrent episode process. One example
is the medical cost related to hospitalization, where each hospitalization
serves as a single observation. For the problem, we present a joint analysis
approach for regression analysis of both longitudinal and observation processes and
a simulation study is conducted that assesses the finite sample performance
of the approach. The asymptotic properties of the proposed estimates are also
given and the method is applied to the medical cost data that motivated this study.
|Jae Woo Jeong, Miami University, Hamilton Ohio|
|Isogeometric analysis of plates with cracks|
|ABSTRACT: The mapping techniques for isogeometric analysis, introduced by
Jeong et al. (2013), is an effective method for dealing with crack singularities of elliptic boundary value problems. In some sense, the mapping techniques is similar to the Method of Auxiliary Mapping(MAM), introduced by Babuska and Oh (1990), for conventional Finite Element Methods(FEM). However, unlike MAM, the mapping techniques make it possible to independently control the radial and angular direction of the function to be approximated as far as the point singularities are concerned.The vertical displacement of a thin plate is governed by a fourth order elliptic equation and thus the approximation functions for numerical solutions are required to have continuous partial derivatives. Hence, the conventional FEM has difficulties to solve the fourth order problems. In order to deal a plate problem with crack effectively, the approximation functions must be smooth except at the crack tip and have singularity at the crack. In this talk, I will discuss recent results and ongoing works on isogeometric analysis, including a way to construct such approximation functions.
|Margaret Readdy, University of Kentucky|
|Counting, q-counting and negative q-counting|
|ABSTRACT: Given a mathematical object, one can simply count it. A more sophisticated method of enumeration, called a q-analogue, is to count an object by keeping track of one or more of its mathematical properties. When setting q=1, one returns to the naive enumeration. After reviewing some classical q-analogues, I will discuss the new idea of a negative q-analogue. This will include recent work of Fu, Reiner, Stanton and Thiem on the negative q-binomial coefficient, and, time permitting, new work of Cai and Readdy on negative q-Stirling numbers.|
|Megan Wawro, Virginia Tech|
|A realistic approach to instruction in linear algebra|
|ABSTRACT: The purpose of this study is to investigate how students conceptualize span and linear (in)dependence, and to utilize the construct of mathematical activity to provide insight into these conceptualizations. The data under consideration are portions of individual interviews with students in an inquiry-oriented linear algebra course. Through grounded analysis via the framework of concept image (Tall & Vinner, 1991), the range of student conceptions of span and linear (in)dependence are organized into four concept image categories: travel, geometric, vector algebraic, and matrix algebraic. To further illuminate participants’ conceptions, a framework was developed to classify engagement in types of mathematical activity: defining, proving, relating, example generating, and problem solving. The coordinated analysis of concept image with engagement in mathematical activity facilitates a nuanced and rich characterization of students’ connections within and between the concepts of span and linear (in)dependence. The talk will include a brief description of the curricular materials, based on the instructional design theory of Realistic Mathematics Education (Freudenthal, 1991), that were implemented within this linear algebra course.|
|Dimplekumar Chalishajar, Virginia Military Institute|
|Exact controllability of second order impulsive neutral differential inclusion with infinite delay in Banach spaces|
|ABSTRACT: Controllability is one of the fundamental tools of applied differential equations and differential inclusions. I will discuss about the exact controllability of second order impulsive neutral differential inclusion with infinite delay in the Banach spaces. Also we will discuss the glitch in the infinite dimension space. Then I will discuss the new notion of control theory called trajectory-controllability, in finite and infinite dimension spaces. Finally the numerical estimations of the same trajectory control problem will be discussed.|