Mathematical Biology Seminar - Spring 2020 | Department of Mathematical Sciences

For questions about the seminar schedule, please contact James Maclaurin

Date	Speaker, Affiliation, and Title	Host
Febrauary 12	Shane Kepley, Rutgers University Computing Global Dynamics for Biological Networks Please note this seminar will be held on a Wednesday, 1:30pm to 2:30pm in CULM 505 Modeling the global dynamics of biological networks requires understanding system parameters. For biological networks of interest, these parameters are both high dimensional and difficult to measure which makes this task difficult. To further complicate matters, collecting data often requires expensive experiments and therefore ground truth data is sparse. In this talk we will present a generally applicable combinatorial framework for studying global dynamics which aims to overcome some of these issues. We will illustrate the approach with examples and show how this methodology has revealed surprising connections between dynamical systems, algebraic geometry, and order theory which are still being explored.	Roy Goodman
February 18	Saskia Haegens, Columbia University & Donders Institute Oscillatory Building Blocks Underlying Perception & Cognition In daily life, we receive a continuous stream of information. This sensory input has to be filtered and processed when relevant, while irrelevant or distracting input has to be suppressed. In my view, oscillations provide the scaffolding for information transfer, and understanding these oscillatory mechanisms is critical to understanding higher-level cognitive functions. The oscillatory building blocks I consider here, and their proposed mechanistic roles, are: (i) slow oscillations in the delta/theta bands (1–7 Hz), providing selective sampling of sensory input, (ii) the alpha rhythm (8–14 Hz), involved in active functional inhibition, and (iii) beta oscillations (15–30 Hz), forming transient, flexible neural ensembles. My lab studies these oscillatory mechanisms in the context of attention and perceptual decision-making, using a combination of techniques including spike and LFP recordings, ECoG, MEG, and psychophysics.	Amitabha Bose
February 25	Ulises Obilinovic, New York University Attractors, Chaos, Sequences and Meta-Stable Attractors in Recurrent Networks Endowed with Hebbian Plasticity During behavior, cortical circuits display a diverse repertoire of neuronal dynamics, including persistent activity, sequences, meta-stable states, and heterogeneous activity. It has been hypothesized that such dynamics could arise from unsupervised learning processes in which the synaptic strengths are modified via Hebbian plasticity from random synaptic inputs. In this talk, I will present a modeling framework in which I systematically explore this hypothesis. Throughout the talk, I will highlight insights from the mean-field theories developed for analyzing these networks. First, I will present a recurrent network model endowed with Hebbian plasticity in which both learning rules and the distribution of stored patterns are inferred from distributions of visual responses for novel and familiar images in the monkey inferior temporal cortex (ITC). We show that two types of retrieval states exist: one in which firing rates are constant in time (fixed-point attractors), and another in which firing rates fluctuate chaotically. Consistent with what has been observed in ITC, fixed-point attractor retrieval states exhibit distributions of firing rates that are close to lognormal, while chaotic retrieval states present irregular temporal dynamics that strongly resemble the temporal variability observed during delay periods in the frontal cortex. Second, I will describe the effect of introducing temporally asymmetry in the learning process. In this scenario, instead of fixed-point or chaotic attractors, the network naturally learns sequences of activity reflected in the transient correlation of network activity with each of the stored input patterns. Interestingly, sequences maintain robust decodability, but display highly labile dynamics, when synaptic connectivity is continuously modified due to noise or storage of other patterns, similar to recent observations in the hippocampus and parietal cortex. Finally, I will show that low-dimensional correlated variability leads to sequences of meta-stable attractors in a network endowed with both a temporally symmetric and asymmetric learning processes. The dynamics displayed by this network recapitulates several statistical features extracted from recordings in the rat motor cortex during self-initiated behavior, suggesting a new neuronal mechanism for accounting the behavioral variability underlying self-initiated actions.	James Maclaurin
March 30	Canceled	James Maclaurin

Updated: May 6, 2020