I have been concerned with understanding how humans sense, remember, and move in their environment. To do so, I have studied mathematical equations that model activity in the brain responsible for these processes. One specific process I have studied recently is short term memory. If you want to remember something small for a period of a few seconds, like a telephone number, you would engage short, rather than long, term memory. A natural question that arises is how best the brain may set up a network of neurons to do this, especially because memory fades with time. What I have found is that there is a trade-off between the number of things that you are capable of storing and how well the memory of those things persist. If you want to be able to remember something for a fairly long time (this would be like a minute for short term memory), you have to have a network that is only capable of storing a few different possibilities. To be able to store a wide variety of things, the trade-off is you will not be able to remember for very long. All these results have implications for the treatment of age related short term memory loss. I have also looked at methods for treating epileptic seizures. One way to do this would be to implant an electrode in the brain of a person with chronic epilepsy, kind of like a pacemaker. The trick is to provide the proper electrical stimulation based on the characteristics of the seizure. Doing so requires sophisticated mathematical techniques.
