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I'll show how these quantities can determine the extent to which the given probability measure can be decomposed as an equal weight mixture of two probability measures with significantly different second order statistics. Joint work with Joe Kileel and Vandy Tombs.", "occurrence_notes":null, "guid":"147094-21900372@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/147094", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"4088", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics"], "website":"https:\/\/sites.google.com\/view\/probsemumich\/future-talks", "sponsors":[ { "group_name":"Probability and Analysis Seminar - Department of Mathematics", "group_id":"5203", "website":"https:\/\/sites.google.com\/view\/probsemumich\/future-talks" }, { "group_name":"Department of Mathematics", "group_id":"3791", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", 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Joint work with Ilya Gekhtman, Wenyuan Yang and Tianyi Zheng.", "occurrence_notes":null, "guid":"146361-21898956@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/146361", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"3866", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics"], "website":"", "sponsors":[ { "group_name":"RTG Seminar on Geometry, Dynamics and Topology - Department of Mathematics", "group_id":"4900", "website":"" }, { "group_name":"Department of Mathematics", "group_id":"3791", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21898956 } , "147412-21900990": { "datetime_modified":"20260405T225946", "datetime_start":"20260408T160000", "datetime_end":"20260408T170000", "has_end_time":1, "date_start":"2026-04-08", "date_end":"2026-04-08", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Student AIM Seminar: Spatially informed biologically interpretable machine learning approaches for analyzing EEG data", "occurrence_title":"", "combined_title":"Student AIM Seminar: Spatially informed biologically interpretable machine learning approaches for analyzing EEG data: Madelyn Cruz", "event_subtitle":"Madelyn Cruz", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"Biological neural networks (BNNs) are machine learning models that enhance the biological interpretability of artificial neural networks by modeling neural dynamics and providing insights underlying neural system behavior. In our previous work, Hodgkin-Huxley neuron models were implemented in BNNs to classify electroencephalogram (EEG) signals. While biologically interpretable, these models treat each electrode independently and ignore spatial relationships, limiting their ability to capture large-scale brain dynamics.\n\nHere, we develop trainable BNNs using time-aware backpropagation applied to networks of biophysically accurate neurons based on modified Hodgkin-Huxley equations, integrated within feedforward and recurrent architectures. Neuron sets represent brain regions, and synaptic weights reflect spatial distances and functional connectivity. These BNNs classify consciousness levels from EEG data, extrapolate deeper brain activity, and exhibit physiologically observed frequencies, while hidden-layer neurons remain biologically interpretable. 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