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1. A Computational Study of a Spatiotemporal Mean Field Model Capturing the Emergence of Alpha and Gamma Rhythmic Activity in the Neocortex

   https://doi.org/10.3390/sym10110568  

   Haddad, Wassim (November 2018, Symmetry)

   In this paper, we analyze the spatiotemporal mean field model developed by Liley et al. in order to advance our understanding of the wide effects of pharmacological agents and anesthetics. Specifically, we use the spatiotemporal mean field model for capturing the electrical activity in the neocortex to computationally study the emergence of α - and γ -band rhythmic activity in the brain. We show that α oscillations in the solutions of the model appear globally across the neocortex, whereas γ oscillations can emerge locally as a result of a bifurcation in the dynamics of the model. We solve the dynamic equations of the model using a finite element solver package and show that our results verify the predictions made by bifurcation analysis. 

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2. Optogenetic stimulation shifts the excitability of cerebral cortex from type I to type II: oscillation onset and wave propagation

   Heitmann, S.; Rule, M.; Truccolo, W.; Ermentrout, B. (January 2017, PLOS computational biology)

   Constant optogenetic stimulation targeting both pyramidal cells and inhibitory interneurons has recently been shown to elicit propagating waves of gamma-band (40–80 Hz) oscillations in the local field potential of non-human primate motor cortex. The oscillations emerge with non-zero frequency and small amplitude—the hallmark of a type II excitable medium—yet they also propagate far beyond the stimulation site in the manner of a type I excitable medium. How can neural tissue exhibit both type I and type II excitability? We investigated the apparent contradiction by modeling the cortex as a Wilson-Cowan neural field in which optogenetic stimulation was represented by an external current source. In the absence of any external current, the model operated as a type I excitable medium that supported propagating waves of gamma oscillations similar to those observed in vivo. Applying an external current to the population of inhibitory neurons transformed the model into a type II excitable medium. The findings suggest that cortical tissue normally operates as a type I excitable medium but it is locally transformed into a type II medium by optogenetic stimulation which predominantly targets inhibitory neurons. The proposed mechanism accounts for the graded emergence of gamma oscillations at the stimulation site while retaining propagating waves of gamma oscillations in the non-stimulated tissue. It also predicts that gamma waves can be emitted on every second cycle of a 100 Hz oscillation. That prediction was subsequently confirmed by re-analysis of the neurophysiological data. The model thus offers a theoretical account of how optogenetic stimulation alters the excitability of cortical neural fields. 

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3. Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission

   https://doi.org/10.3934/mbe.2022393  

   Chen, Lin; Wu, Xiaotian; Xu, Yancong; Rong, Libin (January 2022, Mathematical Biosciences and Engineering)

   In this paper, an insect-parasite-host model with logistic growth of triatomine bugs is formulated to study the transmission between hosts and vectors of the Chagas disease by using dynamical system approach. We derive the basic reproduction numbers for triatomine bugs and Trypanosoma rangeli as two thresholds. The local and global stability of the vector-free equilibrium, parasite-free equilibrium and parasite-positive equilibrium is investigated through the derived two thresholds. Forward bifurcation, saddle-node bifurcation and Hopf bifurcation are proved analytically and illustrated numerically. We show that the model can lose the stability of the vector-free equilibrium and exhibit a supercritical Hopf bifurcation, indicating the occurrence of a stable limit cycle. We also find it unlikely to have backward bifurcation and Bogdanov-Takens bifurcation of the parasite-positive equilibrium. However, the sustained oscillations of infected vector population suggest that Trypanosoma rangeli will persist in all the populations, posing a significant challenge for the prevention and control of Chagas disease. 

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4. Dynamic predictive coding: A model of hierarchical sequence learning and prediction in the neocortex

   https://doi.org/10.1371/journal.pcbi.1011801  

   Jiang, Linxing Preston; Rao, Rajesh_P N (February 2024, PLOS Computational Biology)

   Rubin, Jonathan (Ed.)

   We introduce dynamic predictive coding, a hierarchical model of spatiotemporal prediction and sequence learning in the neocortex. The model assumes that higher cortical levels modulate the temporal dynamics of lower levels, correcting their predictions of dynamics using prediction errors. As a result, lower levels form representations that encode sequences at shorter timescales (e.g., a single step) while higher levels form representations that encode sequences at longer timescales (e.g., an entire sequence). We tested this model using a two-level neural network, where the top-down modulation creates low-dimensional combinations of a set of learned temporal dynamics to explain input sequences. When trained on natural videos, the lower-level model neurons developed space-time receptive fields similar to those of simple cells in the primary visual cortex while the higher-level responses spanned longer timescales, mimicking temporal response hierarchies in the cortex. Additionally, the network’s hierarchical sequence representation exhibited both predictive and postdictive effects resembling those observed in visual motion processing in humans (e.g., in the flash-lag illusion). When coupled with an associative memory emulating the role of the hippocampus, the model allowed episodic memories to be stored and retrieved, supporting cue-triggered recall of an input sequence similar to activity recall in the visual cortex. When extended to three hierarchical levels, the model learned progressively more abstract temporal representations along the hierarchy. Taken together, our results suggest that cortical processing and learning of sequences can be interpreted as dynamic predictive coding based on a hierarchical spatiotemporal generative model of the visual world. 

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5. A Stochastic Analysis of Queues with Customer Choice and Delayed Information

   https://doi.org/10.1287/moor.2019.1024  

   Pender, Jamol; Rand, Richard; Wesson, Elizabeth (August 2020, Mathematics of Operations Research)

   Many service systems provide queue length information to customers, thereby allowing customers to choose among many options of service. However, queue length information is often delayed, and it is often not provided in real time. Recent work by Dong et al. [Dong J, Yom-Tov E, Yom-Tov GB (2018) The impact of delay announcements on hospital network coordination and waiting times. Management Sci. 65(5):1969–1994.] explores the impact of these delays in an empirical study in U.S. hospitals. Work by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] uses a two-dimensional fluid model to study the impact of delayed information and determine the exact threshold under which delayed information can cause oscillations in the dynamics of the queue length. In this work, we confirm that the fluid model analyzed by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] can be rigorously obtained as a functional law of large numbers limit of a stochastic queueing process, and we generalize their threshold analysis to arbitrary dimensions. Moreover, we prove a functional central limit theorem for the queue length process and show that the scaled queue length converges to a stochastic delay differential equation. Thus, our analysis sheds new insight on how delayed information can produce unexpected system dynamics. 

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