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Mingzhou Ding

Publications and source records attributed to Mingzhou Ding.

18 recordsLinked to original sources

Associative Emotional Learning in Convolutional Neural Networks

Associative emotional learning enables organisms to adaptively link pleasant or unpleasant outcomes to the presence of predictive stimuli. Whereas computational models such as the Rescorla-Wagner model have shed light on this important function, the limitations of these models are also known, especially when they are applied to neural data. The advent of deep neural networks has opened another avenue for modeling associative emotional learning. In this work we proposed a deep neural network model of visual valence processing, consisting of a visual module that encodes complex natural scenes and a module that recognizes their emotional significance in terms of valence, a key dimension of emotion, and tested a novel Pavlovian learning paradigm on the model. The results showed that with learning, the model reproduced several observations from human associative learning studies, including association formation and generalization, and that the neural representations of the conditioned and the unconditioned stimuli became increasingly aligned both at the single unit and at the neural population level. Comparison between the model and human experimental data provided further validation of our approach. This study thus suggests that deep neural network models, when combined with appropriate learning algorithms, can be used to model behavioral and neural signatures of associative emotion/valence learning.

cs.AI

Spiked Laplacian Graphs: Bayesian Community Detection in Heterogeneous Networks

In network data analysis, it is becoming common to work with a collection of graphs that exhibit \emph{heterogeneity}. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify communities, and graph Laplacian-based methods are routinely used. However, these methods are currently limited to a single network and do not provide measures of uncertainty on the community assignment. In this work, we propose a probabilistic network model called the ``Spiked Laplacian Graph'' that considers each network as an invertible transform of the Laplacian, with its eigenvalues modeled by a modified spiked structure. This effectively reduces the number of parameters in the eigenvectors, and their sign patterns allow efficient estimation of the community structure. Further, the posterior distribution of the eigenvectors provides uncertainty quantification for the community estimates. Subsequently, we introduce a Bayesian non-parametric approach to address the issue of heterogeneity in a collection of graphs. Theoretical results are established on the posterior consistency of the procedure and provide insights on the trade-off between model resolution and accuracy. We illustrate the performance of the methodology on synthetic data sets, as well as a neuroscience study related to brain activity in working memory. Keywords: Hierarchical Community Detection, Isoperimetric Constant, Mixed-Effect Eigendecomposition, Normalized Graph Cut, Stiefel Manifold

stat.ME

Decoding Working Memory Load from EEG with LSTM Networks

Working memory (WM) is a mechanism that temporarily stores and manipulates information in service of behavioral goals and is a highly dynamic process. Previous studies have considered decoding WM load using EEG but have not investigated the contribution of sequential information contained in the temporal patterns of the EEG data that can differentiate different WM loads. In our study, we develop a novel method of investigating the role of sequential information in the manipulation and storage of verbal information at various time scales and localize topographically the sources of the sequential information based decodability. High density EEG (128-channel) were recorded from twenty subjects performing a Sternberg verbal WM task with varying memory loads. Long Short-Term Memory Recurrent Neural Networks (LSTM-RNN) were trained to decode memory load during encoding, retention, activity-silent, and retrieval periods. Decoding accuracy was compared between ordered data and a temporally shuffled version that retains pattern based information of the data but not temporal relation to assess the contribution of sequential information to decoding memory load. The results show that (1) decoding accuracy increases with increase in the length of the EEG time series given to the LSTM for both ordered and temporally shuffled cases, with the increase being faster for ordered than temporally shuffled time series, and (2) according to the decoding weight maps, the frontal, temporal and some parietal areas are an important source of sequential information based decodability. This study, to our knowledge, is the first study applying a LSTM-RNN approach to investigate temporal dynamics in human EEG data in encoding WM load information.

q-bio.NC

Spatio-temporal Granger causality: a new framework

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and precisely estimate the Granger causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger causality from fMRI, EEG, and other related data.

stat.AP

Mitigating the effects of measurement noise on Granger causality

Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the dynamical organization of the system being investigated. Since experimental measurements are inevitably contaminated by noise, it is thus important to understand the effects of such noise on Granger causality estimation. The first goal of this paper is to provide an analytical and numerical analysis of this problem. Specifically, we show that, due to noise contamination, (1) spurious causality between two measured variables can arise and (2) true causality can be suppressed. The second goal of the paper is to provide a denoising strategy to mitigate this problem. Specifically, we propose a denoising algorithm based on the combined use of the Kalman filter theory and the Expectation-Maximization (EM) algorithm. Numerical examples are used to demonstrate the effectiveness of the denoising approach.

physics.data-an

Estimating Granger causality from Fourier and wavelet transforms of time series data

Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data. Here, we extend the framework of nonparametric spectral methods to include the estimation of Granger causality spectra for assessing directional influences. We illustrate the utility of the proposed methods using synthetic data from network models consisting of interacting dynamical systems.

physics.data-an

Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data

It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger causality analysis may not clearly distinguish between direct causal influences from one time series to another and indirect ones acting through a third time series. In order to differentiate direct from indirect Granger causality, a conditional Granger causality measure in the frequency domain is derived based on a partition matrix technique. Simulations and an application to neural field potential time series are demonstrated to validate the method.

q-bio.NC

Granger Causality: Basic Theory and Application to Neuroscience

Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized that neural interactions are directional. Being able to assess the directionality of neuronal interactions is thus a highly desired capability for understanding the cooperative nature of neural computation. Research over the last few years has shown that Granger causality is a key technique to furnish this capability. The main goal of this article is to provide an expository introduction to the concept of Granger causality. Mathematical frameworks for both bivariate Granger causality and conditional Granger causality are developed in detail with particular emphasis on their spectral representations. The technique is demonstrated in numerical examples where the exact answers of causal influences are known. It is then applied to analyze multichannel local field potentials recorded from monkeys performing a visuomotor task. Our results are shown to be physiologically interpretable and yield new insights into the dynamical organization of large-scale oscillatory cortical networks.

q-bio.QM

Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present a general methodology to yield explicit constraints on the coupling strengths to ensure the stability of the equilibrium point. Two models of coupled excitatory-inhibitory oscillators are used to illustrate the approach.

cond-mat.dis-nn

Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such relations. In this work we consider nonlinear extensions of Granger's idea and refer to the result as Extended Granger Causality. A simple approach implementing the Extended Granger Causality is presented and applied to multiple chaotic time series and other types of nonlinear signals. In addition, for situations with three or more time series we propose a conditional Extended Granger Causality measure that enables us to determine whether the causal relation between two signals is direct or mediated by another process.

nlin.CD

Generalized Turing Patterns and Their Selective Realization in Spatiotemporal Systems

We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we show that these spatial patterns can be selectively realized by varying the coupling strengths along different paths in the parameter space. Furthermore, we discuss the important role of the synchronized state (fixed point versus chaotic attractor) in modulating the temporal dynamics of the spatial patterns.

nlin.PS

General Stability Analysis of Synchronized Dynamics in Coupled Systems

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on the master stability function and Gershgorin disc theory, to yield constraints on the coupling strengths to ensure the stability of synchronized dynamics. Systems with specific coupling schemes are used as examples to illustrate our general method.

nlin.CD

Separation of multiple evoked responses using differential amplitude and latency variability

In neuroelectrophysiology one records electric potentials or magnetic fields generated by ensembles of synchronously active neurons in response to externally presented stimuli. These evoked responses are often produced by multiple generators in the presence of ongoing background activity. While source localization techniques or current source density estimation are usually used to identify generators, application of blind source separation techniques to obtain independent components has become more popular. We approach this problem by applying the Bayesian methodology to a more physiologically-realistic source model. As it is generally accepted that single trials vary in amplitude and latency, we incorporate this variability into the model. Rather than making the unrealistic assumption that these cortical components are independent of one another, our algorithm utilizes the differential amplitude and latency variability of the evoked waveforms to identify the cortical components. The algorithm is applied to intracortically-recorded local field potentials in monkeys performing a visuomotor task.

physics.med-ph

Stability of Synchronized Chaos in Coupled Dynamical Systems

We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on coupling strengths which ensure the stability of synchronized chaos. Previous results in this area involving particular coupling schemes (e.g. global coupling and nearest neighbor diffusive coupling) are included as special cases of the present work.

nlin.CD

First passage time problem for biased continuous-time random walks

We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform of the FPT density function when the bias is constant. When the bias depends linearly on the position, the full FPT density function is derived in terms of Hermite polynomials and generalized Mittag-Leffler functions.

cond-mat.stat-mech

First Passage Time Distribution for Anomalous Diffusion

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exemplified by the fractional Brownian motion, we show that the two types of anomalous diffusions give rise to two distinct scaling behavior.

cond-mat.stat-mech

An integrated approach to the assessment of long range correlation in time series data

To assess whether a given time series can be modeled by a stochastic process possessing long range correlation one usually applies one of two types of analysis methods: the spectral method and the random walk analysis. The first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results. We thus advocate an integrated approach which requires the use of both methods in a consistent fashion. We provide the theoretical foundation of this approach and illustrate the main ideas using examples. The second objective relates to the observation of long range anticorrelation (Hurst exponent H < 1/2) in real world time series data. The very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur. Using examples we discuss the possible factors that could contribute to the false claim of long range anticorrelations and demonstrate the particular importance of the integrated approach in this case.

cond-mat.stat-mech

Anomalous diffusion and the first passage time problem

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H-functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.

cond-mat.stat-mech