The effectiveness, robustness, and flexibility of memory and learning constitute the very essence of human natural intelligence, cognition, and consciousness. However, currently accepted views on ...these subjects have, to date, been put forth without any basis on a true physical theory of how the brain communicates internally via its electrical signals. This lack of a solid theoretical framework has implications not only for our understanding of how the brain works, but also for wide range of computational models developed from the standard orthodox view of brain neuronal organization and brain network derived functioning based on the Hodgkin-Huxley ad-hoc circuit analogies that have produced a multitude of Artificial, Recurrent, Convolution, Spiking, etc., Neural Networks (ARCSe NNs) that have in turn led to the standard algorithms that form the basis of artificial intelligence (AI) and machine learning (ML) methods. Our hypothesis, based upon our recently developed physical model of weakly evanescent brain wave propagation (WETCOW) is that, contrary to the current orthodox model that brain neurons just integrate and fire under accompaniment of slow leaking, they can instead perform much more sophisticated tasks of efficient coherent synchronization/desynchronization guided by the collective influence of propagating nonlinear near critical brain waves, the waves that currently assumed to be nothing but inconsequential subthreshold noise. In this paper we highlight the learning and memory capabilities of our WETCOW framework and then apply it to the specific application of AI/ML and Neural Networks. We demonstrate that the learning inspired by these critically synchronized brain waves is shallow, yet its timing and accuracy outperforms deep ARCSe counterparts on standard test datasets. These results have implications for both our understanding of brain function and for the wide range of AI/ML applications.
A network of propagating nonlinear oscillatory modes (waves) in the human brain is shown to generate collectively synchronized spiking activity (hypersynchronous spiking) when both amplitude and ...phase coupling between modes are taken into account. The nonlinear behavior of the modes participating in the network are the result of the nonresonant dynamics of weakly evanescent cortical waves that, as shown recently, adhere to an inverse frequency-wave number dispersion relation when propagating through an inhomogeneous anisotropic media characteristic of the brain cortex. This description provides a missing link between simplistic models of synchronization in networks of small amplitude phase coupled oscillators and in networks built with various empirically fitted models of pulse or amplitude coupled spiking neurons. Overall the phase-amplitude coupling mechanism presented in the Letter shows significantly more efficient synchronization compared to current standard approaches and demonstrates an emergence of collective synchronized spiking from subthreshold oscillations that neither phase nor amplitude coupling alone are capable of explaining.
An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of nonevanescent (weakly damped) wave-like modes propagating in the thin cortex layers ...transverse to both the mean neural fiber direction and the cortex spatial gradient. Although the amplitude of these modes stays below the typically observed axon spiking potential, the lifetime of these modes may significantly exceed the spiking potential inverse decay constant. Full-brain numerical simulations based on parameters extracted from diffusion and structural MRI confirm the existence and extended duration of these wave modes. Contrary to the commonly agreed paradigm that the neural fibers determine the pathways for signal propagation in the brain, the signal propagation because of the cortex wave modes in the highly folded areas will exhibit no apparent correlation with the fiber directions. Nonlinear coupling of those linear weakly evanescent wave modes then provides a universal mechanism for the emergence of synchronized brain wave field activity. The resonant and nonresonant terms of nonlinear coupling between multiple modes produce both synchronous spiking-like high-frequency wave activity as well as low-frequency wave rhythms. Numerical simulation of forced multiple-mode dynamics shows that, as forcing increases, there is a transition from damped to oscillatory regime that can then transition quickly to a nonoscillatory state when a critical excitation threshold is reached. The resonant nonlinear coupling results in the emergence of low-frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling. The localization and persistence of these weakly evanescent cortical wave modes have significant implications in particular for neuroimaging methods that detect electromagnetic physiological activity, such as EEG and magnetoencephalography, and for the understanding of brain activity in general, including mechanisms of memory.
Purpose
A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented.
Methods
This ...method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods.
Results
Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition.
Conclusions
The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.
Analytical expressions for scaling of brain wave spectra derived from the general non-linear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of ...the weakly evanescent non-linear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different non-linear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order non-linear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.
Purpose
The ability to register image data to a common coordinate system is a critical feature of virtually all imaging studies. However, in spite of the abundance of literature on the subject and ...the existence of several variants of registration algorithms, their practical utility remains problematic, as commonly acknowledged even by developers of these methods.
Methods
A new registration method is presented that utilizes a Hamiltonian formalism and constructs registration as a sequence of symplectomorphic maps in conjunction with a novel phase space regularization. For validation of the framework a panel of deformations expressed in analytical form is developed that includes deformations based on known physical processes in MRI and reproduces various distortions and artifacts typically present in images collected using these different MRI modalities.
Results
The method is demonstrated on the three different magnetic resonance imaging (MRI) modalities by mapping between high resolution anatomical (HRA) volumes, medium resolution diffusion weighted MRI (DW‐MRI) and HRA volumes, and low resolution functional MRI (fMRI) and HRA volumes.
Conclusions
The method has shown an excellent performance and the panel of deformations was instrumental to quantify its repeatability and reproducibility in comparison to several available alternative approaches.
Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental “neuronal avalanche” data. The theory of ...the weakly evanescent nonlinear brain wave dynamics Phys. Rev. Research 2, 023061 (2020); J. Cognitive Neurosci. 32, 2178 (2020) reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.
A primary goal of many neuroimaging studies that use magnetic resonance imaging (MRI) is to deduce the structure-function relationships in the human brain using data from the three major neuro-MRI ...modalities: high-resolution anatomical, diffusion tensor imaging, and functional MRI. To date, the general procedure for analyzing these data is to combine the results derived independently from each of these modalities.
In this article, we develop a new theoretical and computational approach for combining these different MRI modalities into a powerful and versatile framework that combines our recently developed methods for morphological shape analysis and segmentation, simultaneous local diffusion estimation and global tractography, and nonlinear and nongaussian spatial-temporal activation pattern classification and ranking, as well as our fast and accurate approach for nonlinear registration between modalities. This joint analysis method is capable of extracting new levels of information that is not achievable from any of those single modalities alone. A theoretical probabilistic framework based on a reformulation of prior information and available interdependencies between modalities through a joint coupling matrix and an efficient computational implementation allows construction of quantitative functional, structural, and effective brain connectivity modes and parcellation.
This new method provides an overall increase of resolution, accuracy, level of detail, and information content and has the potential to be instrumental in the clinical adaptation of neuro-MRI modalities, which, when jointly analyzed, provide a more comprehensive view of a subject’s structure-function relations, while the current standard, wherein single-modality methods are analyzed separately, leaves a critical gap in an integrated view of a subject’s neuorphysiological state. As one example of this increased sensitivity, we demonstrate that the jointly estimated structural and functional dependencies of mode power follow the same power law decay with the same exponent.
Abstract
The detection of complex spatially and temporally varying coherent structures in data from highly nonlinear and non-Gaussian systems is a challenging problem in a wide range of scientific ...disciplines. This is the case in the analysis of Doppler on Wheels (DOW) mobile Doppler radar (MDR) data where the goal is to detect rapidly evolving coherent storm structures that reflect the complex interplay of nonlinear dynamical processes. Estimating and quantifying such structures from the noisy and relatively sparsely sampled MDR data poses a difficult inverse problem for which traditional analysis methods such as expert and subjective pattern recognition, thresholding, and contouring choices can be difficult. In this paper the authors investigate the application of a recently developed objective method for the analysis of spatiotemporal data called the entropy field decomposition (EFD) to the problem of the analysis of MDR data in tornadic supercells. The EFD method is based on a field theoretic reformulation of Bayesian probability theory that incorporates prior information from the coupling structure within the data to automatically detect multivariate spatiotemporal modes. The method is first applied to data from a numerically simulated tornadic supercell in order to validate the method’s ability to detect and quantify known storm-scale features. It is then applied to actual MDR data collected during the evolution of a tornadic supercell—data that have been analyzed previously by experts. The authors demonstrate the ability of the EFD method to detect spatiotemporal features currently believed to be related to tornadogenesis. This new method has the potential to provide improved and objective analysis/detection with increased sensitivity to nonlinear and non-Gaussian spatially and temporally coherent features related to tornadogenesis and thus offers the potential to aid in the study, prediction, and warnings of tornadoes.
As computed tomography and related technologies have become mainstream tools across a broad range of scientific applications, each new generation of instrumentation produces larger volumes of ...more-complex 3D data. Lagging behind are step-wise improvements in computational methods to rapidly analyze these new large, complex datasets. Here we describe novel computational methods to capture and quantify volumetric information, and to efficiently characterize and compare shape volumes. It is based on innovative theoretical and computational reformulation of volumetric computing. It consists of two theoretical constructs and their numerical implementation: the spherical wave decomposition (SWD), that provides fast, accurate automated characterization of shapes embedded within complex 3D datasets; and symplectomorphic registration with phase space regularization by entropy spectrum pathways (SYMREG), that is a non-linear volumetric registration method that allows homologous structures to be correctly warped to each other or a common template for comparison. Together, these constitute the Shape Analysis for Phenomics from Imaging Data (SAPID) method. We demonstrate its ability to automatically provide rapid quantitative segmentation and characterization of single unique datasets, and both inter-and intra-specific comparative analyses. We go beyond pairwise comparisons and analyze collections of samples from 3D data repositories, highlighting the magnified potential our method has when applied to data collections. We discuss the potential of SAPID in the broader context of generating normative morphologies required for meaningfully quantifying and comparing variations in complex 3D anatomical structures and systems.
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