## April 2014

**Harold J. Gay Lecture-Viorel Barbu (University of Iasi, Romania)-PDEs and variational based models for image restoring**

Friday, 4/25/2014 3:00 PM-5:00 PM

Kaven Hall, 116

ABSTRACT: One surveys here a few nonlinear diffusion models in image restoration and denoising with main emphasis on that described by nonlinear parabolic equations of gradient type. The well-posedness of the corresponding Cauchy problem as well as stability of the derived finite difference scheme is studied from perspectives of nonlinear semigroup theory. Most of denoising PDE procedures existing in literature, though apparently are efficient at experimental level, are however mathematically ill posed and our effort here is to put them on more rigorous mathematical basis.

For more information, e-mail ma-chair@wpi.edu.

**Special Colloquium-Jo Ellis-Monaghan-(Saint Michael's College and the University of Vermont.)-DNA Origami and the Complexity of Eulerian Circuits with Turning Costs**

Monday, 4/28/2014 4:00 PM-5:00 PM

Kaven Hall, 116

ABSTRACT:In 1994, Adelman gave a proof-of-concept for biomolecular computing by demonstrating a selfassembling DNA tetrahedron and using a biomolecular process to find a Hamilton cycle. Since then, instances of several other classical NP-Hard problems, such as 3-SAT and graph coloring, have been solved through biomolecular computing processes using DNA self-assembly. The first step in such a problem is designing the input, that is, self-assembling a graph out of strands of DNA. One of the most successful recent techniques for self-assembly of graph-theoretical structures from DNA molecules is by origami folding, which involves finding a route for the scaffolding strand through the desired structure. When the target structure is a 1-complex (or the geometric realization of a graph), an optimal route corresponds to an Eulerian circuit through the graph with minimum turning cost. By showing that it leads to a solution to the 3-SAT problem, we prove that the general problem of finding an optimal route for a scaffolding strand for such structures is NPHard. This means that this popular assembly method may not be appropriate for efficient biomolecular computing. We show that the problem may readily be transformed into a Traveling Salesman Problem (TSP), so that the machinery that has been developed for the TSP may be applied to find optimal routes for the scaffolding strand in a DNA origami self-assembly process for other purposes (e.g. medical applications).

This is joint work with Andrew McDowell, Iain Moffatt, and Greta Pangborn.

Jointly sponsored by the Departments of Mathematical Sciences, Biology & Biotechnology, and Physics

For more information, e-mail ma-chair@wpi.edu.

## May 2014

**Colloquium-Rohini Kumar (Wayne State University)-Effect of volatility clustering on the risk indifference price of options**

Friday, 5/2/2014 11:00 AM-12:00 PM

Stratton Hall, 203

ABSTRACT: An indifference pricing of options by convex risk measures was developed by Sircar and Sturm in the paper “From smile asymptotics to market risk measures”. In this pricing method, the option price is given as the solution of backward stochastic differential equations. We look at the effect of volatility clustering on this indifference pricing of options. Volatility clustering is modeled by fast mean-reverting volatility in stochastic volatility models for stock price. Asymptotics of the indifference price of options and their corresponding implied volatility are obtained as the mean-reversion time parameter approaches zero. A correction term to the asymptotic option price and implied volatility are also obtained.

For more information, e-mail ma-chair@wpi.edu.

## April 2014

Harold J. Gay Lecture-Viorel Barbu (University of Iasi, Romania)-PDEs and variational based models for image restoringFriday, 4/25/2014 3:00 PM-5:00 PM

Kaven Hall, 116

ABSTRACT: One surveys here a few nonlinear diffusion models in image restoration and denoising with main emphasis on that described by nonlinear parabolic equations of gradient type. The well-posedness of the corresponding Cauchy problem as well as stability of the derived finite difference scheme is studied from perspectives of nonlinear semigroup theory. Most of denoising PDE procedures existing in literature, though apparently are efficient at experimental level, are however mathematically ill posed and our effort here is to put them on more rigorous mathematical basis.

For more information, e-mail ma-chair@wpi.edu.

Special Colloquium-Jo Ellis-Monaghan-(Saint Michael's College and the University of Vermont.)-DNA Origami and the Complexity of Eulerian Circuits with Turning CostsMonday, 4/28/2014 4:00 PM-5:00 PM

Kaven Hall, 116

ABSTRACT:In 1994, Adelman gave a proof-of-concept for biomolecular computing by demonstrating a selfassembling DNA tetrahedron and using a biomolecular process to find a Hamilton cycle. Since then, instances of several other classical NP-Hard problems, such as 3-SAT and graph coloring, have been solved through biomolecular computing processes using DNA self-assembly. The first step in such a problem is designing the input, that is, self-assembling a graph out of strands of DNA. One of the most successful recent techniques for self-assembly of graph-theoretical structures from DNA molecules is by origami folding, which involves finding a route for the scaffolding strand through the desired structure. When the target structure is a 1-complex (or the geometric realization of a graph), an optimal route corresponds to an Eulerian circuit through the graph with minimum turning cost. By showing that it leads to a solution to the 3-SAT problem, we prove that the general problem of finding an optimal route for a scaffolding strand for such structures is NPHard. This means that this popular assembly method may not be appropriate for efficient biomolecular computing. We show that the problem may readily be transformed into a Traveling Salesman Problem (TSP), so that the machinery that has been developed for the TSP may be applied to find optimal routes for the scaffolding strand in a DNA origami self-assembly process for other purposes (e.g. medical applications).

This is joint work with Andrew McDowell, Iain Moffatt, and Greta Pangborn.

Jointly sponsored by the Departments of Mathematical Sciences, Biology & Biotechnology, and Physics

For more information, e-mail ma-chair@wpi.edu.

## May 2014

Colloquium-Rohini Kumar (Wayne State University)-Effect of volatility clustering on the risk indifference price of optionsFriday, 5/2/2014 11:00 AM-12:00 PM

Stratton Hall, 203

ABSTRACT: An indifference pricing of options by convex risk measures was developed by Sircar and Sturm in the paper “From smile asymptotics to market risk measures”. In this pricing method, the option price is given as the solution of backward stochastic differential equations. We look at the effect of volatility clustering on this indifference pricing of options. Volatility clustering is modeled by fast mean-reverting volatility in stochastic volatility models for stock price. Asymptotics of the indifference price of options and their corresponding implied volatility are obtained as the mean-reversion time parameter approaches zero. A correction term to the asymptotic option price and implied volatility are also obtained.

For more information, e-mail ma-chair@wpi.edu.