In Figure 2A, the clustering coefficient of each node in frequency-specific networks was presented for an AD patient together with MCC of the four-layer networks. As shown, many nodes display quite different values of clustering coefficient across the frequency bands. We also computed the Pearson correlation coefficient of clustering coefficient between each single-layer network and between single-layer and multi-layer networks shown in Figure 2B. Notice that the sequences of clustering coefficient in different layers (band) are uncorrected or weakly anti-corrected, while MCC may show no correlation or weak correlation with clustering coefficient in frequency-specific networks.

Moreover, we computed the multiplex participation coefficient for the time-dependent networks (Figure 7). Since the MPC in frequency-integrated networks depicts the information exchange across frequency bands, the MPC in time-dependent networks can be regarded as an indicator of the global information processing along time. The patients show higher MPC values in the frontal-central area than those in other regions, indicating that the frontal-central area may play a major role in the global information communication within bands over time. Such distinct spatial distribution between groups leads to an increased trend of MPC in the right frontal area and decreased trend in the left posterior area for AD in most frequency bands, though the group difference may not be significant. These results suggest that the node degree distribution of brain networks fluctuates with time and such fluctuations differ among brain regions and between groups.

In Feynman’s path integral, the classical notion of a unique trajectory for a particle is replaced by an infinite sum of classical paths, each weighted differently according to its classical properties. The ultimate result of a functional integrated ecosystem is an exponential creation of consumer value that could not be possible through the individual elements alone, leveraging last-generation connectivity technologies. The conception, design and execution of these kinds of ecosystems represents a completely new dimension of growth enabled by the digital age. We need to look deeper into the results obtained by the pioneers of this integration strategy and frame it in ways that can be measured and applied.

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In this study, we investigated the inter-frequency and temporal dynamics of functional networks in patients with AD. By integrating the frequency-specific networks or time-varying networks with different connectivity patterns, we explored the alteration of the local and global information processing across frequency bands or time in AD. Growing evidence links impairment of brain functions in Alzheimer’s disease (AD) with disruptions of brain functional connectivity. However, whether the AD brain shows similar changes from a dynamic or cross-frequency view remains poorly explored. This paper provides an effective framework to investigate the properties of multiplex brain networks in AD considering inter-frequency and temporal dynamics. Using resting-state EEG signals, two types of multiplex networks were reconstructed separately considering the network interactions between different frequency bands or time points.

This text takes advantage of recent developments in the theory of path integration to provide an improved treatment of quantization of systems that either have no constraints or instead involve constraints with demonstratively improved procedures. Through rapport and respect for the student’s abilities, qualities, and integrity, the teacher creates an environment in which the student can learn in safety and comfort. The lesson https://www.globalcloudteam.com/ is developed, specifically for the student, custom-tailored to the unique circumstances of that particular person, at that particular moment. The student learns how to reorganize their actions in new and more effective ways through the experience of comfort, enjoyment, and ease of movement. The probability for the class of paths can be found by multiplying the probabilities of starting in one region and then being at the next.

Many previous fMRI studies have seen that spontaneous activation of functionally connected brain regions occurs during the resting state, even in the absence of any sort of stimulation or activity. Human subjects presented with a visual learning task exhibit changes in functional connectivity in the resting state for up to 24 hours and dynamic functional connectivity studies have even shown changes in functional connectivity during a single scan. By taking fMRI scans of subjects before and after the learning task, as well as on the following day, it was shown that the activity had caused a resting-state change in hippocampal activity.

We start by reviewing two fundamental principles of brain organisation, namely functional specialisation and functional integration and how they rest upon the anatomy and physiology of cortico-cortical connections in the brain. Section 3 deals with the nature and learning of representations from a theoretical or computational perspective. This section reviews supervised (e.g. connectionist) approaches, information theoretic approaches and those predicated on predictive coding and reprises their heuristics and motivation using the framework of generative models. The key focus of this section is on the functional architectures implied by each model of representational learning. However, it turns out that this is only possible when processes generating sensory inputs are invertible and independent. Invertibility is precluded when the cause of a percept and the context in which it is engendered interact.

- Generative models based on predictive coding solve this problem with hierarchies of backward and lateral projections that prevail in the real brain.
- The results can be of clinical value by helping to identify the regions responsible for psychiatric disorders, as well as to assess how different activities or lifestyles affect the functioning of the brain.
- (A) ROC analysis with the features of cross-frequency networks (top) and time-varying networks (bottom).
- The theme of context-sensitive evoked responses is generalised to a cortical level and human functional neuroimaging studies in the subsequent section.
- As illustrated in Figure 1A, the time series of EEG are segmented into non-overlapping time windows of width 4 s, functional connectivity is assessed in each window and thus we can generate a multilayer network, where each layer denotes a certain time point.

Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of particles and fields. The studies involving human participants were reviewed and approved by the Ethics committee of Tangshan Gongren hospital. The patients/participants provided their written informed consent to participate in this study. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature.

These extra-classical phenomena have implications for theoretical ideas about how the brain might work. This review uses the relationship among theoretical models of representational learning as a vehicle to illustrate how imaging can be used to address important questions about functional brain architectures. Our intent was to characterize the abnormalities of information exchange in the multiplex brain networks for AD patients. Nevertheless, we also recognized the fact that AD may have different stages and show heterogeneous characteristics among the patients. Moreover, tracking the change of brain activities from mild cognitive impairment (MCI) to AD is also an interesting topic in AD research and needs future investigation. These investigations should be performed on larger cohorts of patients with different cognitive levels and using other experimental paradigms.

(B) The heat map represents the correlation of node clustering coefficient sequence between frequency-specific networks or between frequency-specific and cross-frequency networks. Notice that the node clustering coefficient in multiplex network may be uncorrected or weakly correlated with that in frequency-specific networks. Namely, the appreciation that functional specialisation exhibits similar extra-classical phenomena in which a cortical area may be specialised for one thing in one context but something else in another.

I’ll be working towards a doctorate, undertaking research into how modern enterprises manage their ecosystems. My particular area of interest is the logic of ‘functional integration,’ for companies managing a portfolio of business models focused on building high value for their consumers. When two signals are completely connected with a stable phase difference, niPLV reaches the upper bound 1.

As two basic properties in human connectome, brain integration, and segregation enable flexible and efficient flow of information within local regions and across the whole brain. Relationships between these properties and the cognitive decline progression were also observed (Kabbara et al., 2018). However, most of these studies are focused on the global information processing (integration) but neglected the local information processing (segregation) across frequency bands. Moreover, all these investigations were performed in a static view and the temporal dynamics were not considered in AD. We hypothesized that in AD brain, altered integration and segregation can be found not only across frequency bands but also over time, and such information can be applied to detect AD. Therefore, we construct both cross-frequency and time-dependent networks using multilayer network theory.

The averaged MCC (left panel) and MPC (right panel) in time-varying networks (in broadband) across the subjects with different number of layers (window length is 4 s). These studies can be cross-validated by attempting to locate and assess patients with lesions or other damage in the identified brain region, and examining whether they exhibit functional deficits relative to the population. In an ordinary integral (in the sense of Lebesgue integration) there is a function to be integrated (the integrand) and a region of space over which to integrate the function (the domain of integration).

This inconsistency can also be found for the normalized clustering coefficient (relative to the random networks). As a metric reflecting global information processing, the participation coefficient is also widely used to measure the diversity of inter-modular connections (Kabbara et al., 2018). A reduction of gamma inter-modular connectivity has also been found in patients with AD (Guillon et al., 2017). Similar to the clustering coefficient in the single-layer network that describes the tendency to form locally dense clusters or modules, MCC can be applied to characterize the tendency of network nodes to form locally connected triangles across different layers. Therefore, higher MCC values may indicate increased efficiency of information flow in corresponding clusters (local brain regions) across frequency bands or time.