Applied Math Seminar

Spring 2015 Schedule

Location: Minard 220
Time: Monday (with the exception of the first TWO presentations), 4:00-4:50 pm
Organizer: Indranil SenGupta



Previous years: Fall 2014, Spring 2014
May 4, 2015 (Monday)
Sylvio May, Physics, NDSU: Theory and Monte Carlo Simulations of Self-Assembly in Dilute Solutions

This talk discusses how to model the self-assembly of particles under dilute conditions and compares the model predictions with Monte Carlo simulations. A number of applications will be mentioned, including dimerization, linear growth, and cooperative assembly with a critical concentration. There are many real-world applications to the formalism, like chemical reactions, the mass action law, so-called living polymers, and peptides forming pores in bacterial membranes.
April 20, 2015 (Monday)
Kevin Kissi (Undergraduate student), Mathematics, NDSU: Solvability of matrix Riccati inequalities

We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati inequalities is a subject of the famous Kalman- Yakubovich lemma. This talk presents necessary and sufficient conditions for solvability of Riccati inequality in the general sign indefinite case. To this end we use special representations of Hamiltonian matrices. The results are illustrated by an example.
April 13, 2015 (Monday)
Semere Habtemicael (Graduate student), Mathematics, NDSU: Modeling Financial derivatives using the BN-S Model

Swap is a financial derivative in which two counter parties exchange cash flows of financial instrument. Variance and volatility swaps are becoming increasingly popular in financial market. These are financial instruments that provide an easy way for investors to gain exposure to the future level of volatility. In this presentation we use non-Gaussian Ornstein-Uhlenbeck process driven by Levy subordinators to model the dynamics of stock price and used this model to price variance, volatility, covariance and correlation swaps. We use S&P500 index data for our regression fit.
March 30, 2015 (Monday)
Nikita Barabanov, Mathematics, NDSU: Optimal control for finite dimensional dynamical systems (Part III)

March 23, 2015 (Monday)
Nikita Barabanov, Mathematics, NDSU: Optimal control for finite dimensional dynamical systems (Part II)

March 9, 2015 (Monday)
Nikita Barabanov, Mathematics, NDSU: Optimal control for finite dimensional dynamical systems (Part I)

We consider the standard Linear Quadratic and H-infinity control problems in state space and frequency domains. The subject of the talk concerns approaches based on Nehari problem and Riccati equations with associated Hamiltonian matrices.
March 2, 2015 (Monday)
Guilherme Volpe Bossa (Graduate student), Physics, NDSU: Nanoparticles at air-water interface: A mixed boundary value problem in spherical geometry

Charged nanoparticles trapped at air-water interface have various applications in materials and biological sciences. Besides the difference of dielectric constants between the media, very often this system is characterized by an asymmetric distribution of charges over the particle surface. To account for these facts and describe the electrostatic potential in all regions , we model the particles as spheres with distinct charge densities at each half: one exposed to the air, where is valid the Laplace equation and the other one exposed to the water, where is valid the non-linear Poisson-Boltzmann equation. By solving a mixed (Robin) boundary value problem this model allows us to predict the effective charge at the air exposed surface and study how the interaction between the particles is affected by their dielectric constant and salt concentration.
February 24, 2015 (Tuesday: Please note the non-regular day)
Sanjay Karmakar, Electrical and Computer Engineering, NDSU: Information Theoretic secrecy in wireless networks (Part II)

February 10, 2015 (Tuesday: Please note the non-regular day)
Sanjay Karmakar, Electrical and Computer Engineering, NDSU: Information Theoretic secrecy in wireless networks (Part I)

A practical communication scenario will be considered where the information/signal exchanged between a legitimate pair (Say Bob and Alice) is also observed by an eavesdropping node (Eve). The challenge under this circumstance is to establish an effective and secure communication link between Bob and Alice. The objective is to find the best possible information rate at which reliable communication can take place even in the presence of Eve. Here, the information theoretic approach to attain secrecy will be discussed which is different from the traditional cryptographic approach and therefore, is independent of the computational capabilities of Eve. Starting with a brief description of the relevant yet basic information theoretic tools and/or definitions we shall pose the communication problem as a mathematical optimization problem of a real valued objective function defined over the set of probability distribution functions which satisfy certain well defined condition/s. In this talk, we shall discuss a partial solution of this secret communication problem and also raise some open questions which are interesting in their own right.