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Life Size Medical Brain Model - Human Brain Model - Realistic Brain Anatomy Display, Science Classroom Demonstration Tools (A)

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Hoppensteadt, F. C., and Izhikevich, E. M. (1998). Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use fm radio principles? Biosystems 48, 85–94. doi: 10.1016/S0303-2647(98)00053-7

Kidger, P., Morrill, J., Foster, J., and Lyons, T. (2020). Neural controlled differential equations for irregular time series. arXiv preprint arXiv:2005.08926. doi: 10.48550/arXiv.2005.08926 Recurrent neural networks (RNN) are the Turing-complete ( Kilian and Siegelmann, 1996) algorithms for learning dynamics and are widely used in computational neuroscience. In a nutshell, RNN processes data by updating a “state vector.” The state vector holds the memory across steps in the sequence. This state vector contains long-term information of the sequence from the past steps ( LeCun et al., 2015). DCM can be thought of as a method of finding the optimal parameters of the causal relations that best fit the observed data. The parameters of the connectivity network are (1) anatomical and functional couplings, (2) induced effect of stimuli, and (3) the parameters that describe the influence of the input on the intrinsic couplings. The expectation-maximization (EM) algorithm is the widely-used optimizer. However, EM is slow for large, changing, and/or noisy networks. Zhuang et al. (2021) showed Multiple-Shooting Adjoint Method for Whole-Brain Dynamic outperforming EM on classification tasks while being used for continuous and changing networks. Beurle, R. L.. (1956). Properties of a mass of cells capable of regenerating pulses. Philos. Trans. R. Soc. Londo. B Biol. Sci. 240, 55–94. doi: 10.1098/rstb.1956.0012 Haken, H.. (2006). Information and Self-Organization: A Macroscopic Approach to Complex Systems. Springer Series in Synergetics, 3rd Edn. Springer-Verlag.A reservoir computer (RC) ( Maass et al., 2002) is an RNN with a reservoir of interconnected spiking neurons. Broadly speaking, the distinction of RC among RNNs, in general, is the absence of granular layers between input and output. RCs themselves are dynamical systems that help learn the dynamics of data. Traditionally, the units of a reservoir have nonlinear activation functions that allow them to be universal approximators. Gauthier et al. (2021) show that this nonlinearity can be consolidated in an equivalent nonlinear vector autoregressor. With the nonlinear activation function out of the picture, the required computation, data, and metaparameter optimization complexity are significantly reduced, the interpretability is consequently improved while the performance stays the same. 3.1.2.4. Liquid State Machine Whole-brain phenomenological models like the Virtual Brain ( Sanz Leon et al., 2013) are conventional generators for reconstructing spontaneous brain activity. There are various considerations to have in mind to choose the right model for the right task. A major trade-off is between the complexity and abstractiveness of the parameters ( Breakspear, 2017). In other words, to capture the behavior of detailed cytoarchitectural and physiological make-up with a reasonably-parametrized model. Another consideration is the incorporation of noise, which is a requirement for multistable behavior ( Piccinini et al., 2021) i.e., transitions between stable patterns of reverberating activity (aka attractors) in a neural population in response to perturbation ( Kelso, 2012). 2.2.1.2. Kuramoto

It is not easy to define what a complex system is. Haken (2006) defines the degree of complexity of a sequence as the minimum length of the program and of the initial data that a Turing machine (aka the universal computer) needs to produce that sequence. Despite being a debatable definition, one can conclude that according to it, the spatiotemporal dynamics of the mammalian brain qualifies as a complex system ( Hutchison et al., 2011; Sforazzini et al., 2014). Therefore, one needs a complex mechanism to reconstruct the neural dynamics. In the following few subsections, we review candidate equations for the oscillations in cortical network ( Buzsáki and Draguhn, 2004). 2.2.1.1. Equilibrium Solutions and Deterministic Chaos There is significant literature on Kuramoto models on neural dynamics on different scales and levels. Strogatz (2000) is a conceptual review of decades of research on the principles of the general form of the Kuramoto model. Numerous studies have found consistency between the results from Kuramoto and other classical models in computational neuroscience like Wilson-Cowan ( Wilson and Cowan, 1972; Hoppensteadt and Izhikevich, 1998). Kuramoto model is frequently used for quantifying phase synchrony and for controlling unwanted phase transitions in neurological diseases like epileptic seizures and Parkinson's ( Boaretto et al., 2019). Still, there are many multistability questions regarding cognitive maladaptation yet to be explored, potentially with the help of Kuramoto models and the maps of effective connectivity. Anyaeji et al. (2021) is a review targeting clinical researchers and psychiatrists. It is a good read for learning about the current challenges that could be formulated as a Kuramoto model. Kuramoto is also unique in adaptability to different scales: from membrane resolution with each neuron acting as a delayed oscillator ( Hansel et al., 1995) to the social setting where each subject couples with the other one in the dyad by means of interpersonal interactions ( Dumas et al., 2012). 2.2.1.3. Van der Pol

Kanaa, D., Voleti, V., Kahou, S., Pal, C., and Cifar, M. (2019). “Simple video generation using neural odes,” in Workshop on Learning With Rich Experience, Advances in Neural Information Processing Systems, Vol. 32.

Devor, A., Bandettini, P., Boas, D., Bower, J., Buxton, R., Cohen, L., et al. (2013). The challenge of connecting the dots in the brain. Neuron 80, 270–274. doi: 10.1016/j.neuron.2013.09.008 Phenomenological models: Analogies and behavioral similarities between neural populations and established physical models open the possibility of using well-developed tools in Statistical Physics and Complex Systems for brain simulations. In such models, some priors of the dynamics are given but not by realistic biological assumptions. A famous example is the model of Kuramoto oscillators ( Bahri et al., 2020) in which the goal is to find the parameters that best reconstruct the behavior of the system. These parameters describe the property of the phenomenon (e.g., the strength of the synchrony), although they do not directly express the fabric of the organism.

Coombes, S., beim Graben, P., Potthast, R., and Wright, J. (2014). Neural Fields: Theory and Applications. Springer. Izhikevich, E. M.. (2003). Simple model of spiking neurons. IEEE Trans. Neural Netw. 14, 1569–1572. doi: 10.1109/TNN.2003.820440 Coombes, S., and Byrne, Á. (2019). Next generation neural mass models. Nonlinear Dyn. Comput. Neurosci. 2020, 726–742. doi: 10.1007/978-3-319-71048-8_1 Chang, B., Meng, L., Haber, E., Ruthotto, L., Begert, D., and Holtham, E. (2018). “Reversible architectures for arbitrarily deep residual neural networks,” in Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 32.

HofstoÈtter, C., Mintz, M., and Verschure, P. F. (2002). The cerebellum in action: a simulation and robotics study. Eur. J. Neurosci. 16, 1361–1376. doi: 10.1046/j.1460-9568.2002.02182.x Briggman, K. L., Abarbanel, H. D., and Kristan, W. B. (2005). Optical imaging of neuronal populations during decision-making. Science 307, 896–901. doi: 10.1126/science.1103736 Guest, O., and Martin, A. E. (2020). How computational modeling can force theory building in psychological science. Perspect. Psychol. Sci. 16, 789–802. doi: 10.31234/osf.io/rybh9 Deco, G., Senden, M., and Jirsa, V. (2012). How anatomy shapes dynamics: a semi-analytical study of the brain at rest by a simple spin model. Front. Comput. Neurosci. 6, 68. doi: 10.3389/fncom.2012.00068 In addition to the problem of vanishing and exploding gradients, other pitfalls also demand careful architecture adjustment. Early in the history of deep learning, RNNs demonstrated poor performance on sequences with long-term dependencies ( Schmidhuber, 1992). Long short term memory (LSTM) is specifically designed to resolve this problem. The principle difference of LSTM and vanilla RNN is that instead of a single recurrent layer, it has a “cell” composed of four layers that interact with each other through three gates: input gate, output gate and forget gate. These gates control the flow of old and new information in the “cell state” ( Hochreiter and Schmidhuber, 1997). On certain scales of computation, LSTM still has considerable performance compared to trendy sequential models like transformers. 3.1.2.3. Reservoir ComputingThere are meaningful similarities in brain activity across species. This is especially good news because, unlike humans, neural properties of less-complicated species are well-characterized ( White et al., 1986). Hawrylycz, M., Ng, L., Feng, D., Sunkin, S., Szafer, A., and Dang, C. (2014). “The allen brain atlas,” in Springer Handbook of Bio-Neuroinformatics, 1111–1126. Current generative models fall into three main categories as shown in Figure 1 with respect to their modeling assumption and objective: An integrative example of the implementation discussed above is NeuCube. NueCube is a 3D SNN with plasticity that learns the connections among populations from various STBD modulations such as EEG, fMRI, genetic, DTI, MEG, and NIRS. Gene regulatory networks can be incorporated as well if available. Finally, This implementation reproduces trajectories of neural activity. It has more robustness to noise and higher accuracy in classifying STBD than standard machine learning methods such as SVM ( Kasabov, 2014).

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