110 research outputs found
A mathematical perspective on edge-centric functional connectivity
Edge-centric functional connectivity (eFC) has recently been proposed to
characterise the finest time resolution on the FC dynamics without the
concomitant assumptions of sliding-window approaches. Here, we lay the
mathematical foundations for the edge-centric analysis and examine its main
findings from a quantitative perspective. The proposed framework provides a
theoretical explanation for the observed occurrence of high-amplitude edge
cofluctuations across datasets and clarifies why a few large events drive the
node-centric FC (nFC). Our exposition also constitutes a critique of the
edge-centric approach as currently applied to functional MRI (fMRI) time
series. The central argument is that the existing findings based on edge time
series can be derived from the static nFC under a null hypothesis that only
accounts for the observed static spatial correlations and not the temporal
ones. Challenging our analytic predictions against fMRI data from the Human
Connectome Project confirms that the nFC is sufficient to replicate the eFC
matrix, the edge communities, the large cofluctuations, and the corresponding
brain activity mode. We conclude that the temporal structure of the edge time
series has not so far been exploited sufficiently and encourage further work to
explore features that cannot be explained by the presented static null model
Sum Rates, Rate Allocation, and User Scheduling for Multi-User MIMO Vector Perturbation Precoding
This paper considers the multiuser multiple-input multiple-output (MIMO)
broadcast channel. We consider the case where the multiple transmit antennas
are used to deliver independent data streams to multiple users via vector
perturbation. We derive expressions for the sum rate in terms of the average
energy of the precoded vector, and use this to derive a high signal-to-noise
ratio (SNR) closed-form upper bound, which we show to be tight via simulation.
We also propose a modification to vector perturbation where different rates can
be allocated to different users. We conclude that for vector perturbation
precoding most of the sum rate gains can be achieved by reducing the rate
allocation problem to the user selection problem. We then propose a
low-complexity user selection algorithm that attempts to maximize the high-SNR
sum rate upper bound. Simulations show that the algorithm outperforms other
user selection algorithms of similar complexity.Comment: 27 pages with 6 figures and 2 tables. Accepted for publication in
IEEE Trans. Wireless Comm
Spectral Dynamic Causal Modelling: A Didactic Introduction and its Relationship with Functional Connectivity
We present a didactic introduction to spectral Dynamic Causal Modelling
(DCM), a Bayesian state-space modelling approach used to infer effective
connectivity from non-invasive neuroimaging data. Spectral DCM is currently the
most widely applied DCM variant for resting-state functional MRI analysis. Our
aim is to explain its technical foundations to an audience with limited
expertise in state-space modelling and spectral data analysis. Particular
attention will be paid to cross-spectral density, which is the most distinctive
feature of spectral DCM and is closely related to functional connectivity, as
measured by (zero-lag) Pearson correlations. In fact, the model parameters
estimated by spectral DCM are those that best reproduce the cross-correlations
between all variables--at all time lags--including the zero-lag correlations
that are usually interpreted as functional connectivity. We derive the
functional connectivity matrix from the model equations and show how changing a
single effective connectivity parameter can affect all pairwise correlations.
To complicate matters, the pairs of brain regions showing the largest changes
in functional connectivity do not necessarily coincide with those presenting
the largest changes in effective connectivity. We discuss the implications and
conclude with a comprehensive summary of the assumptions and limitations of
spectral DCM
Secrecy Sum-Rates for Multi-User MIMO Regularized Channel Inversion Precoding
In this paper, we propose a linear precoder for the downlink of a multi-user
MIMO system with multiple users that potentially act as eavesdroppers. The
proposed precoder is based on regularized channel inversion (RCI) with a
regularization parameter and power allocation vector chosen in such a
way that the achievable secrecy sum-rate is maximized. We consider the
worst-case scenario for the multi-user MIMO system, where the transmitter
assumes users cooperate to eavesdrop on other users. We derive the achievable
secrecy sum-rate and obtain the closed-form expression for the optimal
regularization parameter of the precoder using
large-system analysis. We show that the RCI precoder with
outperforms several other linear precoding schemes, and
it achieves a secrecy sum-rate that has same scaling factor as the sum-rate
achieved by the optimum RCI precoder without secrecy requirements. We propose a
power allocation algorithm to maximize the secrecy sum-rate for fixed .
We then extend our algorithm to maximize the secrecy sum-rate by jointly
optimizing and the power allocation vector. The jointly optimized
precoder outperforms RCI with and equal power allocation
by up to 20 percent at practical values of the signal-to-noise ratio and for 4
users and 4 transmit antennas.Comment: IEEE Transactions on Communications, accepted for publicatio
Dynamic causal modelling of COVID-19 and its mitigations
This technical report describes the dynamic causal modelling of mitigated epidemiological outcomes during the COVID-9 coronavirus outbreak in 2020. Dynamic causal modelling is a form of complex system modelling, which uses 'real world' timeseries to estimate the parameters of an underlying state space model using variational Bayesian procedures. Its key contribution-in an epidemiological setting-is to embed conventional models within a larger model of sociobehavioural responses-in a way that allows for (relatively assumption-free) forecasting. One advantage of using variational Bayes is that one can progressively optimise the model via Bayesian model selection: generally, the most likely models become more expressive as more data becomes available. This report summarises the model (on 6-Nov-20), eight months after the inception of dynamic causal modelling for COVID-19. This model-and its subsequent updates-is used to provide nowcasts and forecasts of latent behavioural and epidemiological variables as an open science resource. The current report describes the underlying model structure and the rationale for the variational procedures that underwrite Bayesian model selection
The effect of global signal regression on DCM estimates of noise and effective connectivity from resting state fMRI
The influence of global BOLD fluctuations on resting state functional connectivity in fMRI data remains a topic of debate, with little consensus. In this study, we assessed the effects of global signal regression (GSR) on effective connectivity within and between resting state networks (RSNs) - as estimated with dynamic causal modelling (DCM) for resting state fMRI (rsfMRI). DCM incorporates a forward (generative) model that quantifies the contribution of different types of noise (including global measurement noise), effective connectivity, and (neuro)vascular processes to functional connectivity measurements. DCM analyses were applied to two different designs; namely, longitudinal and cross-sectional designs. In the modelling of longitudinal designs, we considered four extensive longitudinal resting state fMRI datasets with a total number of 20 subjects. In the analysis of cross-sectional designs, we used rsfMRI data from 361 subjects from the Human Connectome Project. We hypothesized that (1) GSR would have no discernible impact on effective connectivity estimated with DCM, and (2) GSR would be reflected in the parameters representing global measurement noise. Additionally, we performed comparative analyses of information gain with and without GSR. Our results showed negligible to small effects of GSR on effective connectivity within small (separately estimated) RSNs. However, although the effect sizes were small, there was substantial to conclusive evidence for an effect of GSR on connectivity parameters. For between-network connectivity, we found two important effects: the effect of GSR on between-network effective connectivity (averaged over all connections) was negligible to small, while the effect of GSR on individual connections was non-negligible. In the cross-sectional (but not in the longitudinal) data, some connections showed substantial to conclusive evidence for an effect of GSR. Contrary to our expectations, we found either no effect (in the longitudinal designs) or a non-specific (cross-sectional design) effect of GSR on parameters characterising (global) measurement noise. Data without GSR were found to be more informative than data with GSR; however, in small resting state networks the precision of posterior estimates was greater after GSR. In conclusion, GSR is a minor concern in DCM studies; however, quantitative interpretation of between-network connections (as opposed to average between-network connectivity) and noise parameters should be treated with some caution. The Kullback-Leibler divergence of the posterior from the prior (i.e., information gain) - together with the precision of posterior estimates - might offer a useful measure to assess the appropriateness of GSR in resting state fMRI
Dynamic causal modelling of fluctuating connectivity in resting-state EEG
Functional and effective connectivity are known to change systematically over time. These changes might be explained by several factors, including intrinsic fluctuations in activity-dependent neuronal coupling and contextual factors, like experimental condition and time. Furthermore, contextual effects may be subject-specific or conserved over subjects. To characterize fluctuations in effective connectivity, we used dynamic causal modelling (DCM) of cross spectral responses over 1- min of electroencephalogram (EEG) recordings during rest, divided into 1-sec windows. We focused on two intrinsic networks: the default mode and the saliency network. DCM was applied to estimate connectivity in each time-window for both networks. Fluctuations in DCM connectivity parameters were assessed using hierarchical parametric empirical Bayes (PEB). Within-subject, between-window effects were modelled with a second-level linear model with temporal basis functions as regressors. This procedure was conducted for every subject separately. Bayesian model reduction was then used to assess which (combination of) temporal basis functions best explain dynamic connectivity over windows. A third (betweensubject) level model was used to infer which dynamic connectivity parameters are conserved over subjects. Our results indicate that connectivity fluctuations in the default mode network and to a lesser extent the saliency network comprised both subject-specific components and a common component. For both networks, connections to higher order regions appear to monotonically increase during the 1- min period. These results not only establish the predictive validity of dynamic connectivity estimates - in virtue of detecting systematic changes over subjects - they also suggest a network-specific dissociation in the relative contribution of fluctuations in connectivity that depend upon experimental context. We envisage these procedures could be useful for characterizing brain state transitions that may be explained by their cognitive or neuropathological underpinnings
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