Understanding the brain is one of the most fascinating current endeavors in science. In the last decades, with the advent of modern experimental and computational techniques, physicists are increasingly helping to decipher some of the brain's learning mechanisms. Yet, there is much to be determined about how it processes and learns information. Despite many brain processing models, no detailed systematic efforts to fit them to experimental behavioral data exist. Little attempt is made to connect such behavioral data with emerging phenomena, such as consciousness.
In collaboration with Pat Suppes, Claudio Carvalhaes, and Gary Oas, we started research goals to bridge the behavior and brain gap. To do that, we are begun with models for behavioral stimulus-response (SR) theory. This theory has a solid mathematical foundation. Its central concept of conditioning can be easily generalized to the more complex idea of association. Thus, it is an ideal starting point for connecting psychology experiments with neural modeling. Our goal is to set constraints from macroscopic signals. One could narrow down the characteristics of the underlying model for brain processing. For instance, we modeled SR theory with neural oscillators and compared our results with experiments in the literature.
Another question that we are investigating, in collaboration with Zyg Pizlo, is the relation between perception and minimization theorems. It is well-known in physics that most of modern physics can be derived from variational principles. These principles state that the minimization of the action leads to the equations of motion. Our question is whether similar ideas apply to perception. For example, in visual perception, the minimization of a cost function leads to the three-dimensional reconstruction of objects. Would this idea and its consequences, such as Noether's theorem, apply to other perception problems? If so, what would we learn from it? What other problems would be suggested by it?
Finally, I have also been interested in the relationship between the brain and mind. How can the mind be an emergent concept formed from the brain's interconnected network of neurons? Since neurons are made of quantum particles, how can the mind's identity follow from matter that lacks identity itself? Is there a relationship between the underlying quantum world and how it feels to be ourselves? Those types of questions are part of my research in collaboration with Carlos Montemayor.
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