Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration; prerequisites consist mostly of some basic knowledge of quantum mechanics. Business model configurations are especially important in technology-based environments where firms often require distinct business models that operate in tandem to develop multiple revenue streams with the same technology. Thus there is a need to frame a growth strategy pattern that leads to the creation of functionally integrated ecosystems. The ability to visualize whole-brain activity is frequently used in comparing brain function during various sorts of tasks or tests of skill, as well as in comparing brain structure and function between different groups of people.

To further assess the possible application of multiplex network metrics in detecting AD, we implemented classification analysis based on the multiplex graph features on local scales. Considering the fact that high-dimensional input may increase the computational cost and lead to overfitting in the classification, we applied feature extraction and selection techniques to improve the classification performance. Only the features with significant group difference were considered in the classification process. After that, the least absolute shrinkage and selection operator (LASSO) logistic regression algorithm was applied to select the most significant predictive features and remove redundant features.

The theme of context-sensitive evoked responses is generalised to a cortical level and human functional neuroimaging studies in the subsequent section. The critical focus of this section is evidence for the interaction of bottom–up and top–down influences in determining regional brain responses. The final section reviews some of the implications of the forgoing sections for lesion studies and neuropsychology.

## An optimal estimation approach to visual perception and learning

Unlike the clustering coefficient of a static graph, the multiplex clustering coefficient describes how likely the nodes tend to cluster between any two time points. In fact, for a complex system, the local information communication between elementary entities may take a relatively long time rather than being completed within a short time window. Therefore, MCC can be applied to describe the properties of local information processing across time and provide additional information different from those obtained by looking at the clustering in a static network. In this study, both groups show uniform distribution of MCC among brain regions, implying that these regions may play different roles in the local specialized processing of information over time. Moreover, for the patients, significant decrease of MCC was found in the delta and beta bands, particularly in the left occipital area. This suggests that the local communication efficiency of the dynamic network is also selectively disrupted in AD.

The authors develop six propositions on how cross‐functional integration affects performance and test the propositions in an international sample of 266 manufacturing plant organizations in nine countries. By comparing the first experimental task to the second, as well as to the control group, the study authors observed that the brain region most significantly activated by the task requiring phonological storage was the supramarginal gyrii. This result was backed up by previous literature observations of functional deficits in patients with damage in this area. Functional integration was developed by Percy John Daniell in an article of 1919[1] and Norbert Wiener in a series of studies culminating in his articles of 1921 on Brownian motion. They developed a rigorous method (now known as the Wiener measure) for assigning a probability to a particle’s random path. Richard Feynman developed another functional integral, the path integral, useful for computing the quantum properties of systems.

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.

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.

## Multiplex Functional Network Construction

This is important in relation to functional asymmetries in forward and backward connections that have been demonstrated empirically. Different from the participation coefficient describing integration of different modules or communities, MPC denotes the heterogeneity of connectivity patterns (nodal degree distribution) in each layer. From a statistical view, a random walker reaching nodes with high MPC values will jump to any other layers with similar properties. Hence, higher MPC values may facilitate the global information processing across layers with increased efficiency. (A) ROC analysis with the features of cross-frequency networks (top) and time-varying networks (bottom).

This result confirms that MCC may provide important information different from those obtained within frequency bands. As a metric quantifying the integration in a multiplex network, MPC describes the global information exchange between different frequency-specific networks. It can be applied to evaluate the regional centrality of a cross-frequency network, as the nodes with high MPC values allow a random walker jump with similar probability to other layers and thus facilitate the information transmission across frequency bands. We found that AD brain may show decreased integration in the posterior area resulting from altered spatial distribution of MPC.

## Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms

(B) Scatter plot shows the Mahalanobis distance of each sample from AD or control class with the combination of MCC and MPC in the time-varying networks (gray line indicates equal distance). The best performance was achieved by the combination of MCC and MPC in the time-varying networks. (A) The node clustering coefficient of the frequency-specific networks and cross-frequency networks for a representative patient.

We provided a common framework to investigate integration and segregation properties in these networks using two multiplex graph metrics. These measures can provide rich information about how information was processed or transferred across frequency bands (time) in global brain or local brain regions. Finally, we tested the diagnostic power of the multiplex network dynamics to discriminate AD patients and healthy controls. In the present study, we extended the framework of brain network analysis by the investigation of information communication in functional networks from a dynamic view. Multiplex clustering coefficient was employed as a dynamic graph metric to study the local information processing over time.

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 https://www.globalcloudteam.com/ 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.

- This enforces an explicit parameterisation of generative models (i.e. backward connections) to enable approximate recognition and suggests that feedforward architectures, on their own, are not sufficient.
- During the progression of disease, the patients may exhibit decreased hub centrality or number of hubs (Yu et al., 2017).
- Considering the fact that high-dimensional input may increase the computational cost and lead to overfitting in the classification, we applied feature extraction and selection techniques to improve the classification performance.
- Therefore, the AD brain cannot be simply characterized by declined or enhanced information processing in the dynamic networks.
- Moreover, we combined the segregation and integration properties in the cross-frequency networks to get a more complete picture of the inter-frequency dynamics for AD.

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. As the most common cause of dementia, Alzheimer’s disease (AD) is a disabling neurodegenerative disorder characterized by progressive impairment of learning, memory, and other cognitive functions. 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).

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.

In fact, Equation (6) contains information about the fraction of triads centered in i that close into triangles and the weight of edges in the triangles. It is demonstrated that all the classifiers exhibit promising results with over 90% accuracy. In particular, the SVM and discriminant analysis classifier show similar results with an averaged accuracy of 92.5%. The algebraic properties of functional integrals are used to develop series used to calculate properties in quantum electrodynamics and the standard model of particle physics.