WIM Lecture Series

**When:** Thursday April 24th, 2014 at 12:15pm

**Where:** OLIN 107

**Speaker:** Alicia Prieto Langarica, Department of Mathematics and Statistics, Youngstown State University

**Title:** Upscaling Discrete to Continuous Mathematical Models (and other Interesting things in Mathematical Biology)

**Abstract:** In this talk we consider two interacting populations: individuals and stimulus. Individuals move in response to the stimulus population while the stimulus only diffuses. Both populations grow while the stimulus population is being depleted by the individuals. In order to account for the random nature of the system, an individual-based model (IBM) is first developed and then upscaled into a continuous partial differential equation(PDE) model by considering transition probabilities for the individuals at each site. The model we are proposing is very general and has numerous applications in biology and many other sciences. In addition we will talk about multiple applications of mathematics to biology and social sciences.

Students of all levels, areas, and genders are welcome!

Refreshments will be served at 12:05pm.

**WIM Lecture Series**

**When:** Monday March 17th, 2014 at 12:15pm

**Where:** ZOOK 310

**Speaker:** Alethea Barbaro, Department of Mathematics, Case Western Reserve University

**Title:** Simulating Social Dynamics with Interacting Particle Models

**Abstract:** Consider a group of social animals. In many such contexts, members of the group will come together to undertake and perform a task which an individual is unable to do alone. Explaining why these groups form and how they function presents opportunities for some very exciting interdisciplinary research. In this talk, I will discuss how we use an interacting particle system together with environmental data to simulate and predict migration routes of a species of fish around Iceland. I will discuss scaling laws which we propose for this type of interacting particle model in order to keep the global dynamics the same while varying the number of particles used in the simulation. I will also discuss my research on gang dynamics, where we use an agent-based model of the gangs in Los Angeles to reproduce the rivalry network documented by criminologists.

Students of all levels, areas, and genders are welcome!

Refreshments will be served at 12:05pm.

**ORA: Research for Lunch**

**When:** Wednesday March 5th, 2014 at 12:00pm

**Where:** Student Union, Room 316

**Speaker:** Malena Espanol, Department of Mathematics, The University of Akron

**Title:** MRI-based Classifiers for the Detection of Chiari Malformations

**Abstract:** Chiari malformation (CM) is a serious neurological disorder where the bottom part of the brain, the cerebellum, descends out of the skull and crowds the spinal cord, putting pressure on both the brain and spine and causing many symptoms. Magnetic resonance imaging (MRI) is currently an indispensable diagnostic imaging technique in the detection of CM. MRI has dramatically improved the quality of brain pathology diagnosis and treatment. However, there is still a need to develop image analysis tools that can help doctors diagnose CM in a more objective way and that can potentially lead to more reliable and reproducible CM diagnostic procedures. In this talk, we show how machine learning techniques can be used as a tool to identify which MRI features are fundamental for the detection of CM.

Bring your lunch and enjoy a research talk.

**WIM Lecture Series **

**When: **February 27th, 2014 at 12:15pm

**Where: **Crouse Hall 209

**Speaker: **Julianne Chung, Department of Mathematics, Virginia Tech

**Title:** Mathematics, Computing, and Image Processing**Abstract:** An image can be an essential tool in many scientific applications such as biomedical imaging, computational biology, geophysics, astronomy, and video surveillance. For example, in biomedical imaging, good images can be critical for accurate diagnosis and proper treatment of patients. Mathematics and computing play an integral role in the development of good image processing techniques. In this talk, we describe some mathematical models and computational methods for two imaging applications: image deblurring and tomography. In image deblurring, signals measured from machines (e.g., cameras) are distorted, and the aim is to recover the original input signal. In tomography, measurements can only be obtained on the exterior of an object (e.g., the human body or the earth's crust), and the goal is to estimate the internal structures. Both of these are challenging mathematics problems that require robust numerical methods and efficient computation.

Students of all levels, areas, and genders are welcome!

Refreshments will be served at 12:05pm.