Therefore, the AD brain cannot be simply characterized by declined or enhanced information processing in the dynamic networks. Instead, the integration of information at the node level may show more significant difference among brain regions than that between groups. Such spatial difference may also relate to progression of the disease and needs further research. To explore the integration of all frequency components, we first computed the weighted clustering coefficients of the four-layer multiplex networks at both global and local scales.

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.

The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice.

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 https://www.globalcloudteam.com/ 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 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 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.

Most models of representational learning require prior assumptions about the distribution of sensory causes. Using the notion of empirical Bayes, we show that these assumptions are not necessary and that priors can be learned in a hierarchical context. Furthermore, we try to show that learning can be implemented in a biologically plausible way.

(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.

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.

We further applied multiplex network features to characterize functional integration and segregation of the cross-frequency or time-varying networks. Finally, machine learning methods were employed to evaluate the performance of multiplex-network-based indexes for detection of AD. Results revealed that the brain networks of AD patients are disrupted with reduced segregation particularly in the left occipital area for both cross-frequency and time-varying networks. However, the alteration of integration differs among brain regions and may show an increasing trend in the frontal area of AD brain.

These interactions create a problem of contextual invariance that can only be solved using internal or generative models. Contextual invariance is necessary for categorisation of sensory input (e.g. category-specific responses) and represents a fundamental problem in perceptual synthesis. Generative models based on predictive coding solve this problem with hierarchies of backward and lateral projections that prevail in the real brain. In short, generative models of representational learning are a natural choice for understanding real functional architectures and, critically, confer a necessary role on backward connections. A recent EEG network study has also investigated inter-frequency dynamics in AD using multi-layer network metrics (Guillon et al., 2017). They focused on the global information processing across all frequency bands, while in our study, we explored the information exchange between any two bands that may also show abnormalities in AD brain.

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.

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.

- This section compares and contrasts the heuristics behind three prevalent computational approaches to representational learning and perceptual synthesis, supervised learning, and two forms of self-supervised learning based on information theory and predictive coding.
- Earlier studies have suggested that the impairment could arise from focal abnormalities in one or more isolated brain regions such as the entorhinal region or posterior associative cortices (Koenig et al., 2005; Salmon et al., 2005, 2008; He et al., 2009).
- By combining LASSO and multifactor logistic regression, the regression coefficients of most features were set to zero and the features with non-zero coefficients were preserved.
- 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.
- This review summarises approaches to integration in terms of effective connectivity and proceeds to address the question posed by the theoretical considerations above.

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.

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.