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arXiv 2025年

作者： Kasowski, Justin M. Beyeler, Michael Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa BarbaraCA93106 United States Department of Computer Science University of California Santa BarbaraCA93106 United States Department of Psychological & Brain Sciences University of California Santa BarbaraCA93106 United States

Objective: This study systematically evaluates the impact of raster patterns-specific spatial arrangements of sequential electrode activation-on performance and perceived difficulty in simulated prosthetic vision (SPV). By addressing a critical gap in the literature, we aimed to identify patterns that optimize functional vision in retinal implants. Approach: Sighted participants completed letter recognition and motion discrimination tasks under four raster patterns (horizontal, vertical, checkerboard, and random) using an immersive SPV system. The simulations employed psychophysically validated models of electrode activation, phosphene appearance, and temporal dynamics, ensuring realistic representation of prosthetic vision. Performance accuracy and self-reported difficulty were analyzed to assess the effects of raster patterning. Main Results: The checkerboard pattern consistently outperformed other raster patterns, yielding significantly higher accuracy and lower difficulty ratings across both tasks. The horizontal and vertical patterns introduced biases aligned with apparent motion artifacts, while the checkerboard minimized such effects. Random patterns resulted in the lowest performance, underscoring the importance of structured activation. Significance: These findings provide the first systematic evaluation of raster patterns, suggesting that the checkerboard configuration may enhance usability and perceptual clarity in retinal implants. While based on simulated environments, this study establishes a foundation for optimizing spatial and temporal electrode activation strategies in next-generation devices. © 2025, CC BY.

关键词： Prosthetics

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Renormalization group as a Koopman operator

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Physical Review E 2020年第6期101卷 060104(R)-060104(R)页

作者： William T. Redman Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara California 93106 USA

Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents η and δ, as well as ratios of critical exponents, of classical spin systems from single observables alone. This broadens the types of problems that the renormalization group framework can be applied to and establish universality classes of. In addition, this connection may allow for a new, data-driven way in which to find the renormalization group fixed point(s), and their relevant and irrelevant directions.

关键词： dynamical systems Chaos & nonlinear dynamics Critical exponents Renormalization group

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The estrous cycle modulates hippocampal spine dynamics, dendritic processing, and spatial coding

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Neuron 2025年

作者： Wolcott, Nora S. Redman, William T. Karpinska, Marie Jacobs, Emily G. Goard, Michael J. Department of Molecular Cellular and Developmental Biology University of California Santa Barbara Santa Barbara 93106 CA United States Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara Santa Barbara 93106 CA United States Intelligent Systems Center Johns Hopkins University Applied Physics Laboratory Laurel 20723 MD United States Department of Computer Science University of California Santa Barbara Santa Barbara 93106 CA United States Department of Psychological & Brain Sciences University of California Santa Barbara Santa Barbara 93106 CA United States Ann S. Bowers Women's Brain Health Initiative University of California Santa Barbara Santa Barbara 93106 CA United States Neuroscience Research Institute University of California Santa Barbara Santa Barbara 93106 CA United States

Histological evidence suggests that the estrous cycle exerts a powerful influence on CA1 neurons in the mammalian hippocampus. Decades have passed since this landmark observation, yet how the estrous cycle shapes dendritic spine dynamics and hippocampal spatial coding in vivo remains a mystery. Here, we used a custom hippocampal microperiscope and two-photon calcium imaging to track CA1 pyramidal neurons in female mice across multiple cycles. Estrous cycle stage had a potent effect on spine dynamics, with spine density peaking during proestrus when estradiol levels are highest. These morphological changes coincided with greater somatodendritic coupling and increased infiltration of back-propagating action potentials into the apical dendrite. Finally, tracking CA1 response properties during navigation revealed greater place field stability during proestrus, evident at both the single-cell and population levels. These findings demonstrate that the estrous cycle drives large-scale structural and functional plasticity in hippocampal neurons essential for learning and memory. © 2025 The Author(s)

关键词： dendritic integration estradiol estrous cycle hippocampus multiphoton imaging neuroendocrine place cells spine morphology

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Modulation of Dopamine for Adaptive Learning: a Neurocomputational Model

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Computational Brain and Behavior 2021年第1期4卷 34-52页

作者： Inglis, Jeffrey B. Valentin, Vivian V. Ashby, F. Gregory Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara 93106 CA United States Department of Psychological & Brain Sciences University of California Santa Barbara 93106 CA United States

There have been many proposals that learning rates in the brain are adaptive, in the sense that they increase or decrease depending on environmental conditions. The majority of these models are abstract and make no attempt to describe the neural circuitry that implements the proposed computations. This article describes a biologically detailed computational model that overcomes this shortcoming. Specifically, we propose a neural circuit that implements adaptive learning rates by modulating the gain on the dopamine response to reward prediction errors, and we model activity within this circuit at the level of spiking neurons. The model generates a dopamine signal that depends on the size of the tonically active dopamine neuron population and the phasic spike rate. The model was tested successfully against results from two single-neuron recording studies and a fast-scan cyclic voltammetry study. We conclude by discussing the general applicability of the model to dopamine-mediated tasks that transcend the experimental phenomena it was initially designed to address. © 2020, Society for Mathematical Psychology.

关键词： Adaptive learning rate Computational cognitive neuroscience Dopamine Ventral subiculum

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On Koopman mode decomposition and tensor component analysis

arXiv

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arXiv 2021年

作者： Redman, William T. Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara CA93106 United States

Koopman mode decomposition and tensor component analysis (also known as CANDECOMP/PARAFAC or canonical polyadic decomposition) are two popular approaches of decomposing high dimensional data sets into modes that capture the most relevant features and/or dynamics. Despite their similar goal, the two methods are largely used by different scientific communities and are formulated in distinct mathematical languages. We examine the two together and show that, under certain conditions on the data, the theoretical decomposition given by tensor component analysis is the same as that given by Koopman mode decomposition. This provides a "bridge" with which the two communities should be able to more effectively communicate. Our work provides new possibilities for algorithmic approaches to Koopman mode decomposition and tensor component analysis, and offers a principled way in which to compare the two methods. Additionally, it builds upon a growing body of work showing that dynamical systems theory, and Koopman operator theory in particular, can be useful for problems that have historically made use of optimization theory. © 2021, CC BY.

关键词： Clustering algorithms

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Control of ecological outcomes through deliberate parameter changes in a model of the gut microbiome

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Physical Review E 2020年第5期101卷 052402-052402页

作者： Zipeng Wang Eric W. Jones Joshua M. Mueller Jean M. Carlson Department of Physics University of California Santa Barbara Santa Barbara California 93106 USA Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara Santa Barbara California 93106 USA

The generalized Lotka-Volterra (gLV) equations are a mathematical proxy for ecological dynamics. We focus on a gLV model of the gut microbiome, in which the evolution of the gut microbial state is determined in part by pairwise interspecies interaction parameters that encode environmentally mediated resource competition between microbes. We develop an in silico method that controls the steady-state outcome of the system by adjusting these interaction parameters. This approach is confined to a bistable region of the gLV model. In this method, a dimensionality reduction technique called steady-state reduction (SSR) is first used to generate a two-dimensional (2D) gLV model that approximates the high-dimensional dynamics on the 2D subspace spanned by the two steady states. Then a bifurcation analysis of the 2D model analytically determines parameter modifications that drive an initial condition to a target steady state. This parameter modification of the reduced 2D model guides parameter modifications of the original high-dimensional model, resulting in a change of steady-state outcome in the high-dimensional model. This control method, called SSR-guided parameter change (SPARC), bypasses the computational challenge of directly determining parameter modifications in the original high-dimensional system. SPARC could guide the development of indirect bacteriotherapies, which seek to change microbial compositions by deliberately modifying gut environmental variables such as gut acidity or macronutrient availability.

关键词： Complex systems Ecological population dynamics Bacteria dynamical systems High dimensional systems Nonequilibrium systems Coarse graining Phase space dynamics

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Learning Linear Embeddings for Non-Linear Network Dynamics with Koopman Message Passing

arXiv

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arXiv 2023年

作者： Yeh, King Fai Flood, Paris Redman, William Liò, Pietro Department of Computer Science and Technology University of Cambridge United Kingdom Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara United States

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep learning approaches, perform poorly on nonlinear network dynamics problems as they do not address the underlying geometric structure. In this paper we present a novel approach based on Koopman operator theory and message passing networks that finds a linear representation for the dynamical system which is globally valid at any time step. The linearisations found by our method produce predictions on a suite of network dynamics problems that are several orders of magnitude better than current state-of-the-art techniques. We also apply our approach to the highly non-linear training dynamics of neural network architectures, and obtain linear representations which can generate network parameters with comparable performance to networks trained by classical optimisers. © 2023, CC BY.

关键词： Network architecture

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Optimizing neural networks via koopman operator theory 20

Optimizing neural networks via koopman operator theory

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Proceedings of the 34th International Conference on Neural Information Processing Systems

作者： Akshunna S. Dogra William T. Redman John A. Paulson School of Engineering and Applied Sciences Harvard University Cambridge MA Interdeparmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara Santa Barbara CA

ISBN: (纸本)9781713829546

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in making use of this connection. As Koopman operator theory is a linear theory, a successful implementation of it in evolving network weights and biases offers the promise of accelerated training, especially in the context of deep networks, where optimization is inherently a non-convex problem. We show that Koopman operator theoretic methods allow for accurate predictions of weights and biases of feedforward, fully connected deep networks over a non-trivial range of training time. During this window, we find that our approach is >10x faster than various gradient descent based methods (e.g. Adam, Adadelta, Adagrad), in line with our complexity analysis. We end by highlighting open questions in this exciting intersection between dynamical systems and neural network theory, and additional methods by which our results may be generalized.

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Control of ecological outcomes through deliberate parameter changes in a model of the gut microbiome

arXiv

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arXiv 2019年

作者： Wang, Zipeng Jones, Eric W. Mueller, Joshua M. Carlson, Jean M. Department of Physics University of California Santa Barbara Santa BarbaraCA United States Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa Barbara Santa BarbaraCA United States

The generalized Lotka-Volterra (gLV) equations are a mathematical proxy for ecological dynamics. We focus on a gLV model of the gut microbiome, in which the evolution of the gut microbial state is determined in part by pairwise inter-species interaction parameters that encode environmentally-mediated resource competition between microbes. We develop an in silico method that controls the steady-state outcome of the system by adjusting these interaction parameters. This approach is confined to a bistable region of the gLV model. The two steady states of interest are idealized as either a"healthy" or "diseased" steady state of the gut microbiome. In this method, a dimensionality reduction technique called steady-state reduction (SSR) is first used to generate a two-dimensional (2D) gLV model that approximates the high-dimensional dynamics on the 2D subspace spanned by the two steady states. Then a bifurcation analysis of the 2D model analytically determines parameter modifications that drive a disease-prone initial condition to the healthy steady state. This parameter modification of the reduced 2D model guides parameter modifications of the original high-dimensional model, resulting in a change of steady-state outcome in the high-dimensional model. This control method, called SPARC (SSR-guided parameter change), bypasses the computational challenge of directly determining parameter modifications in the original high-dimensional system. SPARC could guide the development of indirect bacteriotherapies, which seek to change microbial compositions by deliberately modifying gut environmental variables such as gut acidity or macronutrient availability. Copyright © 2019, The Authors. All rights reserved.

关键词： Bifurcation (mathematics)

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Local error quantification for efficient neural network dynamical system solvers

arXiv

引用

arXiv 2020年

作者： Dogra, Akshunna S. Redman, William T. John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States Interdepartmental Graduate Program in Dynamical Neuroscience University of California Santa BarbaraCA93106 United States

Neural Networks have been identified as potentially powerful tools for the study of complex systems. A noteworthy example is the Neural Network Differential Equation (NN DE) solver, which can provide functional approximations to the solutions of a wide variety of differential equations. However, there is a lack of work on the role precise error quantification can play in their predictions: most variants focus on ambiguous and/or global measures of performance like the loss function. We address this in the context of dynamical system NN DE solvers, leveraging their learnt information to develop more accurate and efficient solvers, while still pursuing a completely unsupervised, data free approach. We achieve this by providing methods for quantifying the performance of NN DE solvers at local scales, thus allowing the user the capacity for efficient and targeted error correction. We showcase the utility of these methods by testing them on a nonlinear and a chaotic system each. Copyright © 2020, The Authors. All rights reserved.

关键词： Chaotic systems

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