Image segmentation with traveling waves in an exactly solvable recurrent neural network

Proceedings of the National Academy of Sciences, Journal Year: 2025, Volume and Issue: 122(1)

Published: Jan. 3, 2025

We study image segmentation using spatiotemporal dynamics in a recurrent neural network where the state of each unit is given by complex number. show that this generates sophisticated can effectively divide an into groups according to scene’s structural characteristics. then demonstrate simple algorithm for object generalizes across inputs ranging from geometric objects grayscale images natural images. Using exact solution network’s dynamics, we present precise description mechanism underlying providing clear mathematical interpretation how performs task. Object all accomplished with one has single, fixed set weights. This demonstrates expressive potential networks when constructed approach brings together their structure, and computation.

Language: Английский

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Noether symmetry of multi-delay Birkhoffian system and its conserved quantity

AIP Advances, Journal Year: 2025, Volume and Issue: 15(1)

Published: Jan. 1, 2025

The Birkhoffian system, an important mechanical system in analytical mechanics, is studied the background of multiple time delays. Both multi-delay and Hamiltonian are investigated. First, more general framework discussed. Pfaff–Birkhoff action presented with differential equations motion derived for both models. Second, invariance two different kinds Noether symmetries Pfaff studied. Third, due to effects delays, corresponding Noether-type theorems systems obtained. Two examples demonstrate applications results.

Language: Английский

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What do neural travelling waves tell us about information flow?

bioRxiv (Cold Spring Harbor Laboratory), Journal Year: 2025, Volume and Issue: unknown

Published: Feb. 25, 2025

Abstract In many behavioral conditions, neural activity propagates within and across brain regions as traveling waves, revealing the importance of analyzing spatiotemporal dynamics in electrophysiological data. Most methods quantify such propagation by measuring spatial phase gradients, i.e., monotonic ordered changes through space. Here, we demonstrate that ordering travelling waves is insufficient to determine effective flow information unambiguously. We that, some specific cases, gradient indicates opposite direction than indicated for causal inference. Using autoregressive modeling, further show a discrepancy between apparent measured via phase-based can, example, be predicted sign projection from lower higher nodes hierarchy. Together with an input signal lowest node, inhibitory bottom-up connections produce propagating opposite, top-down direction. As methodological solution, Granger causality analysis can recover its underlying structure, which used disambiguate “effective” flow.

Language: Английский

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Bifurcations and collective states of Kuramoto oscillators with higher-order interactions and rotational symmetry breaking

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2025, Volume and Issue: 35(3)

Published: March 1, 2025

We study a network of identical Kuramoto oscillators with higher-order interactions that also break the rotational symmetry system. To gain analytical insights into this model, we use Watanabe–Strogatz Ansatz, which allows us to reduce dimensionality original system equations. The stability and bifurcations reduced reveals codimension two Bogdanov–Takens bifurcation several other associated bifurcations. Such analysis is corroborated by numerical simulations system, which, in turn, unveils variety collective behaviors such as synchronized motion, oscillation death, chimeras, incoherent states, traveling waves. Importantly, displays case where alternating chimeras emerge an indistinguishable single population oscillators, may offer unihemispheric slow-wave sleep phenomenon observed mammals birds.

Language: Английский

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Brain wave dynamics in a Hopfield-Kuramoto model

Physical review. E, Journal Year: 2025, Volume and Issue: 111(4)

Published: April 16, 2025

Whole brain neural oscillation activities exhibit multiple wave phase patterns and seem to be supported by the common circuit network structure. We proposed a Hopfield Kuramoto model based entirely on heterogeneous connectivity strength rather than delay. Multiple can encoded in networks via Hebbian rule retrieved as attractors. systematically investigated how dynamic landscape influenced attractors their corresponding eigenvalues, well control stability of equilibrium points occurrence high dimensional bifurcations. This framework enables us reproduce dominant activity components human functional MRI signal, provides canonical for multi-body physical system spatio-temporal pattern attractor dynamics.

Language: Английский

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An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network

Communications Physics, Journal Year: 2024, Volume and Issue: 7(1)

Published: July 15, 2024

Abstract Networks throughout physics and biology leverage spatiotemporal dynamics for computation. However, the connection between structure computation remains unclear. Here, we study a complex-valued neural network (cv-NN) with linear interactions phase-delays. We report cv-NN displays sophisticated dynamics, which then use, in combination nonlinear readout, The can instantiate dynamics-based logic gates, encode short-term memories, mediate secure message passing through of computations this system be fully described an exact, closed-form mathematical expression. Finally, using direct intracellular recordings neurons slices from neocortex, demonstrate that are decodable by living biological as readout. These results systems perform computations, while also being exactly solvable. Taken together, these open future avenues design highly adaptable, bio-hybrid computing interface seamlessly other networks.

Language: Английский

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Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2023, Volume and Issue: 33(10)

Published: Oct. 1, 2023

Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity dynamical behaviors be used to model study wide range systems. Despite numerous efforts investigate these obtaining mathematical descriptions for the dynamics systems is still an open problem. Here, we combine ideas concepts from linear algebra graph theory nonlinear offer novel approach networks Kuramoto oscillators. Our allows us large, network by decomposing it into two smaller systems: one representing connection scheme within layers (intra-layer), other connections between (inter-layer). Particularly, use this compose solutions These are given combination intra- inter-layer systems, in addition, our stability solutions.

Language: Английский

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Understanding the effect of white matter delays on large scale brain synchrony

Communications in Nonlinear Science and Numerical Simulation, Journal Year: 2023, Volume and Issue: 131, P. 107803 - 107803

Published: Dec. 27, 2023

Language: Английский

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Noether Symmetry of Multi-Time-Delay Non-Conservative Mechanical System and Its Conserved Quantity

Symmetry, Journal Year: 2024, Volume and Issue: 16(4), P. 475 - 475

Published: April 14, 2024

The study of multi-time-delay dynamical systems has highlighted many challenges, especially regarding the solution and analysis equations. symmetry conserved quantity are two important effective essential properties for understanding complex behavior. In this study, a non-conservative mechanical system is investigated. Firstly, Hamilton principle proposed. Then, equations deduced. Secondly, depending on infinitesimal group transformations, invariance action studied, Noether symmetry, quasi-symmetry, generalized quasi-symmetry discussed. Finally, Noether-type quantities Lagrangian obtained. Two examples in terms given.

Language: Английский

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Evolution of neuron firing and connectivity in neuronal plasticity with application to Parkinson’s disease

Physica D Nonlinear Phenomena, Journal Year: 2023, Volume and Issue: 458, P. 133993 - 133993

Published: Nov. 25, 2023

We unify different modeling structures of neuron state evolution showing how they can be derived from an invariance requirement imposed to a dissipation inequality under diffeomorphism-based changes observers in the physical space. This is completely non-standard way using second law thermodynamics, although isothermal setting, otherwise commonly used for determining constitutive restrictions and admissibility conditions as those pertaining shock waves. In this we consider time- varying neuronal connectivity derive consistent structure its equation same principle. case Parkinson, depends also on distribution calcium channels that bring dopamine excess. Under special conditions, show probability time influenced by one channels. account memory effects cortical matter, namely dependence firing histories.

Language: Английский

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