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Background: Intermittent phase synchrony is a phenomenon that occurs at subthreshold levels of oscillator coupling, where two oscillators appear to be synchronized at some times and desynchronized at others. Here, periods of “synchrony” are defined by a certain amount of statistically significant correlation between the time series of the oscillators.1 While general synchrony is observable in any number of settings (e.g. coupled pendula), intermittent synchrony has been detected in EEG readings from specific pairs of electrodes from patients with schizophrenia and Parkinson’s Disease.1 However, the extent to which EEG noise impacts synchrony pattern within the Rubchinsky et. al. model has not yet been studied.1  Methods: Using non-experimental data in MATLAB, we propose to run a series of trials to study the effect of signal-dependent multiplicative noise on the patterns of phase synchrony between oscillators. In the first condition, we simulate two completely synchronized signals, add signal-dependent noise to one, and observe the resulting changes to the synchronization pattern. In the second condition, we begin with two completely desynchronized signals.  Potential Impact: In studies of intermittent phase synchrony, it has been suggested that this pattern is the result of neuronal circuits which, as the EEG signals synchronize, fire more strongly and as a result become less responsive to outside input. This interpretation has the power to explain some of the symptoms experienced by patients. Thus, the specific pattern of synchronized and de-synchronized episodes is potentially highly significant. Our study is a necessary first step to understanding if the existing model and interpretations are accurate.  References: Rubchinsky, L. L., Ahn, S., & Park, C. (2014). Dynamics of desynchronized episodes in intermittent synchronization. Frontiers in Physics, 2. doi:10.3389/fphy.2014.00038 

Background: Although subject to much variation, the anatomy of language comprehension has become increasingly clear with the advent of fMRI; however, the steps of speech comprehension remain elusive. There are two main theories of language processing – hierarchical and sequential (or probabilistic). According to the hierarchical theory, sentences are broken down (e.g. sentence to words to syllables to phonemes) and then reconstructed while syntactic and semantic meanings are attached. Sequential theory suggests the use of “word-level statistics” and n-gram-type models to predict sequences of word meanings.1 Although evidence suggests both models play some role, as a starting point, many comprehension models focus on hierarchical theory, and many of those in turn rely on neural networks. However, in various ways, these models fall short of explaining how the brain can biologically carry out all the steps.  Methods: We attempt to create a hierarchical model of speech comprehension using linear logic (or a related logic) or Category Theory, with the hope that such an approach may be able to explain the process more naturally. We focus on the second half of comprehension (i.e. the reconstruction) to make use of existing neuronal logic gate models.2 The goal is to construct a linear logic model or to create categories and associated functors that could explain hierarchical linguistic processing and many neurolinguistic study results.   Potential Impact: Although this model would only account for hierarchical linguistic processing, it would be a huge step forward in understanding how our brain processes speech – and possibly other inputs – at the level of neuron bundles.  References:  Frank, S. L., Christiansen, M. H. (2018). Hierarchical and sequential processing of language. Language, Cognition and Neuroscience, 1-6. doi:10.1080/23273798.2018.1424347  Goldental, A., Guberman, S., Vardi, R., & Kanter, I. (2014). A computational paradigm for dynamic logic-gates in neuronal activity. Frontiers in Computational Neuroscience, 8. doi:10.3389/fncom.2014.00052 

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From a young age, we are told that being “in sync” is a good thing! From being in sync with the music as we dance to being in sync with teammates on the field, synchronization is celebrated. However, too little or too much synchronization can be bad. In the brain, synchronization allows important information to be sent back and forth between neurons, so that we can make decisions and function in our daily lives. Mathematics can help researchers and doctors understand patterns of abnormal synchronization in the brain and help them to diagnose and potentially treat the symptoms of brain disorders. In this article, we will dive into how mathematics is used to explore and understand the brain—one of our body’s most important organs.