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Nonlinear Dimensionality Reduction Methods in Climate Data Analysis [article]

Ian Ross
2009 arXiv   pre-print
Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets  ...  Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality.  ...  For model reduction methods, there are four possibilities, based on whether the original high-dimensional model is deterministic or stochastic and whether the reduced model is deterministic or stochastic  ... 
arXiv:0901.0537v1 fatcat:2ethc7ddtjdyxkbqzmtg64upwi

The role of slow manifolds in parameter estimation for a multiscale stochastic system with α-stable Lévy noise [article]

Ying Chao, Pingyuan Wei, Jinqiao Duan
2020 arXiv   pre-print
This method provides an advantage in computational complexity and cost, due to the dimension reduction in stochastic systems.  ...  This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian α-stable Lévy noise.  ...  Before using the low dimensional reduction of system (II.1)-(II.2) to estimate parameter λ, we give some results on random slow manifold and its approximation.  ... 
arXiv:2002.11784v1 fatcat:qjpj36mlzvbmzfkkvav2waw3ru

Manifold learning analysis for allele-skewed DNA modification SNPs for psychiatric disorders

Wenbin Liu, Dongdong Li, Henry Han
2020 IEEE Access  
Our results indicate that t-distributed stochastic neighbor embedding (t-SNE) outperforms its peers in distinguishing psychiatric disorder samples from normal ones in both visualization and phenotype classification  ...  We propose a novel manifold learning analysis for ASM-SNP data of bipolar disorder and schizophrenia based on a data-driven feature selection algorithm: nonnegative singular value approximation (NSVA).  ...  E. t-DISTRIBUTED STOCHASTIC NEIGHBOR EMBEDDING (t-SNE) Given a dataset X = {x 1 , x 2 , · · · , x n } in a high-dimensional manifold: x i ∈ R N , t-SNE aims to embed it into a low-dimensional manifold  ... 
doi:10.1109/access.2020.2974292 fatcat:3cl4rzcwa5g3rg2sb4vsyq5kcm

Manifold Optimization Assisted Gaussian Variational Approximation [article]

Bingxin Zhou, Junbin Gao, Minh-Ngoc Tran, Richard Gerlach
2021 arXiv   pre-print
optimizing on manifolds.  ...  To control the computational cost while being able to capture the correlations among the variables, the low rank plus diagonal structure was introduced in the previous literature for the Gaussian covariance  ...  Low Dimensional Predictive Inference We first evaluate our methods on the logistic regression for a low dimensional binary classification problem.  ... 
arXiv:1902.03718v2 fatcat:ov7dk23l5farneoym57guaus2m

Consistent spectral predictors for dynamic causal models of steady-state responses

Rosalyn J. Moran, Klaas E. Stephan, Raymond J. Dolan, Karl J. Friston
2011 NeuroImage  
We then introduce a predictor of spectral activity using centre manifold theory and linear stability analysis.  ...  This predictor is based on sampling the system's Jacobian over the orbits of hidden neuronal states.  ...  To optimise this set of points we test six sampling periods (corresponding to one cycle of a delta, theta, alpha, beta, gamma and high-gamma oscillation).  ... 
doi:10.1016/j.neuroimage.2011.01.012 pmid:21238593 pmcid:PMC3093618 fatcat:2pv2znuexrerxfwnsynyzbwxgy

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

Christian Bick, Marc Goodfellow, Carlo R. Laing, Erik A. Martens
2020 Journal of Mathematical Neuroscience  
Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost.  ...  Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction.  ...  Woldman for helpful feedback on the manuscript, and to R. Mirollo and J. Engelbrecht for helpful discussions.  ... 
doi:10.1186/s13408-020-00086-9 pmid:32462281 fatcat:r35intdfsvcn7li6spbupxwyoa

The Virtual Brain Integrates Computational Modeling and Multimodal Neuroimaging

Petra Ritter, Michael Schirner, Anthony R. McIntosh, Viktor K. Jirsa
2013 Brain Connectivity  
Adding detail to these models will widen their ability to reproduce a broader range of dynamic features of the brain.  ...  Such macroscopic models typically generate only a few selected-ideally functionally relevant-aspects of the brain dynamics.  ...  The three approaches are based on stochastic optimization, state observers, and dimensionality reduction.  ... 
doi:10.1089/brain.2012.0120 pmid:23442172 pmcid:PMC3696923 fatcat:i6677e3cubaqzcbikvczz2uvba

Bayesian inference for stochastic oscillatory systems using the phase-corrected Linear Noise Approximation [article]

Ben Swallow, David A. Rand, Giorgos Minas
2022 arXiv   pre-print
Preliminary analyses based on the Fisher Information Matrix of the model can guide the implementation of Bayesian inference.  ...  We propose a new methodology for inference in stochastic non-linear dynamical systems exhibiting oscillatory behaviour and show the parameters in these models can be realistically estimated from simulated  ...  Relatively vague Gamma(1,10) priors were specified on rate parameters and inverse Gamma IG(0.001,0.001) for the error variance.  ... 
arXiv:2205.05955v1 fatcat:ptm3mfqbq5audfbawwmu5hnpga

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review [article]

Christian Bick, Marc Goodfellow, Carlo R. Laing, Erik Andreas Martens
2020 arXiv   pre-print
Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction.  ...  Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost.  ...  Woldman for helpful feedback on the manuscript, and to R. Mirollo and J. Engelbrecht for helpful discussions.  ... 
arXiv:1902.05307v3 fatcat:u5x2duovcnhrrg4wjvyt452dde

Modeling Dynamic Functional Connectivity with Latent Factor Gaussian Processes [article]

Lingge Li, Dustin Pluta, Babak Shahbaba, Norbert Fortin, Hernando Ombao, Pierre Baldi
2019 arXiv   pre-print
While many methods have been proposed, reliably establishing the presence and characteristics of brain connectivity is challenging due to the high dimensionality and noisiness of neuroimaging data.  ...  The proposed model naturally allows for inference and visualization of time-varying connectivity.  ...  Bayesian latent factor models provide a probabilistic approach to modeling dynamic covariance that allows for simultaneous dimensionality reduction and covariance process estimation.  ... 
arXiv:1905.10413v2 fatcat:knqr3dcxznbg3lyymz5e5z7w6a

Population density equations for stochastic processes with memory kernels

Yi Ming Lai, Marc de Kamps
2017 Physical review. E  
The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly  ...  We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy.  ...  For intrinsically spiking neuronal models, our method bears some similarities to the phase reduction method for oscillators.  ... 
doi:10.1103/physreve.95.062125 pmid:28709222 fatcat:laha47ik4zhatmiao26lohpypm

Dynamically orthogonal field equations for continuous stochastic dynamical systems

Themistoklis P. Sapsis, Pierre F.J. Lermusiaux
2009 Physica D : Non-linear phenomena  
Based on a stochastic reduction on this manifold we derive a stochastic inertial equation that governs the motion of particles and which includes new terms expressing the coupled effect of particles inertia  ...  Based on the stochastic reduction on this manifold we will derive a stochastic inertial equation that governs the motion of particles and which includes new terms expressing the coupled effect of particles  ...  This code is based on the finite-differences numerical scheme and also incorporates the adaptive criteria for the stochastic dimensionality of the solution.  ... 
doi:10.1016/j.physd.2009.09.017 fatcat:c2ri6mttongbpmzaoueu4vg55u

Uncertainty Quantification of Bifurcations in Random Ordinary Differential Equations [article]

Christian Kuehn, Kerstin Lux
2021 arXiv   pre-print
In a first step, we reduce the system's behavior to the dynamics on its center manifold. We thereby still capture the major qualitative behavior of the RODEs.  ...  To realize this major step, we present three approaches: an analytical one, where the probability can be calculated explicitly based on Mellin transformation and inversion, a semi-analytical one consisting  ...  Thus, we perform center manifold reduction for each realization of ω.  ... 
arXiv:2101.05581v2 fatcat:lwomcymdafg2be6i7oxml7as74

Synchronous Chaos and Broad Band Gamma Rhythm in a Minimal Multi-Layer Model of Primary Visual Cortex

Demian Battaglia, David Hansel, Olaf Sporns
2011 PLoS Computational Biology  
This is not easily accounted for in previous network modeling of gamma oscillations. We argue here that interactions between cortical layers can be responsible for this fast decorrelation.  ...  When the stimulus contrast is low, the induced activity is only weakly synchronous and the network resonates transiently without developing collective oscillations.  ...  In this cases, the network dynamics explores a high-dimensional manifold in the phase-space, while, in our model, the irregular sparse firing of many neurons give rise to collective synchronous chaos (  ... 
doi:10.1371/journal.pcbi.1002176 pmid:21998568 pmcid:PMC3188510 fatcat:kwefe7uk3jfuxmepkexj6aemei

Coupling functions: Universal insights into dynamical interaction mechanisms

Tomislav Stankovski, Tiago Pereira, Peter V. E. McClintock, Aneta Stefanovska
2017 Reviews of Modern Physics  
These methods are based on different statistical techniques for dynamical inference.  ...  For instance, it is unclear how to generalize the low-dimensional reduction approach. Networks of chaotic oscillators A subclass of this model offers insight.  ...  Low-dimensional dynamics A particularly striking observation is the low-dimensional dynamics of identical globally coupled phase oscillators under the Sakaguchi-Kuramoto coupling function.  ... 
doi:10.1103/revmodphys.89.045001 fatcat:y53fbhvwc5hoxfhyygetn7cq3a
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