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Functional Integration: Basics and Applications SpringerLink


To ascertain whether backward influences are expressed functionally requires measurements of functional integration among brain systems. This review summarises approaches to integration in terms of effective connectivity and proceeds to address the question posed by the theoretical considerations above. In short, it will be shown that functional neuroimaging can be used to test for interactions between bottom–up and top–down inputs to an area. The conclusion of these studies points toward the prevalence of top–down influences and the plausibility of generative models of sensory brain function.

  • Neuroimaging studies of large numbers of these patients could yield brain activation markers for specific psychiatric illnesses, and also aid in the development of therapeutics and animal models.
  • 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.
  • This inconsistency can also be found for the normalized clustering coefficient (relative to the random networks).
  • 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.
  • In contrast, recent neuroimaging studies have shown that the cognitive deficits in AD is related to pathological changes in large-scale functional or structural networks (Dickerson and Sperling, 2005; Greicius, 2008; Sperling et al., 2009; Pievani et al., 2011).

Only the interactions between the same set of nodes across layers are allowed, so the cross-frequency couplings between different brain regions were not considered. In addition to the four-layer networks including all frequency bands, we also considered the interrelationship of two frequency components to reconstruct two-layer networks (i.e., δ-θ network). For each single-layer network, a data-driven thresholding method was employed by maximizing the global cost efficiency vs. the cost of the surviving functional connections (Bassett et al., 2009). The static graph analysis has proved to be effective in characterizing the disturbed functional connectivity in AD. Many studies investigating the clustering coefficient has showed that the AD brain is characterized by a decrease of clustering in different frequency bands, while other studies may show an opposite trend (Tijms et al., 2013).

The trouble with cognitive subtraction

On the other hand, the alteration of MPC in the time-dependent networks imply that AD brain may operate at a less optimal point in terms of the global information processing along time. In this study, we provided an effective framework to study the functional segregation and integration of brain networks considering inter-frequency and temporal dynamics. In this framework, the patients show decreased segregation particularly in the occipital area, while the alteration of integration differs among brain regions in both cross-frequency and dynamic networks.

functional integration definition

These obtained results gave new insights into the abnormalities of information exchange in brain networks and may benefit our understanding of pathology for AD. On the other hand, reconstructing and analyzing the functional networks in a frequency-integrated or time-varying manner may enrich the methodologies about the deconstruction of brain activity underlying EEG. Future studies will involve the subjects with mild cognitive impairment and be extended to other neurodegenerative diseases. Similar to the MPC of cross-frequency networks that depicts the heterogeneity of global information flow across frequency bands, MPC of the dynamic network reflects the temporal heterogeneity of network information exchange over time. In our study, results exhibited that the efficiency of global information communication differs among brain regions, as both the patients and controls show spatial heterogeneity of MPC in all frequency bands. No significant group difference was found in the MPC at the global level when averaging MPC over all nodes, which can be partly attributed to the fact that the AD network may show an increased trend similar to that in cross-frequency networks.

Towards a theory of early visual processing

Therefore, it is a symmetrical measure and ranges between 0 and 1, with higher values indicating stronger functional interactions. The modern treatment used by the author is an attempt to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. Although fMRI studies of people with schizophrenia and bipolar disorder have yielded some insight into the changes in effective connectivity caused by these diseases,[16] a comprehensive understanding of the functional remodelling that occurs has not yet been achieved.
functional integration
In this study, the non-linear support vector machine (SVM) with a radial basis function kernel was employed as a classifier. Before the training process, the dimension reduction was done by the feature selection technique. To assess the classification performance, we computed the classification accuracy, sensitivity, and specificity. Receiver operating characteristic (ROC) curve was used to test the diagnostic ability of the classifier with varying thresholds, and the corresponding area under the curve (AUC) was also calculated. Since the multiplex networks may consist of different number of layers, we test different combinations of features in the classification process. Functional integration is the study of how brain regions work together to process information and effect responses.
The main point made in this review is that backward connections, mediating internal or generative models of how sensory inputs are caused, are essential if the process generating inputs cannot be inverted. Because these processes are dynamical in nature, sensory inputs correspond to a non-invertible nonlinear convolution of causes. 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. Moreover, nonlinearities in generative models, that induce a dependence on backward connections, require these connections to be modulatory; so that estimated causes in higher cortical levels can interact to predict responses in lower levels.

Classification Analysis

As the static network analysis reflects the average behavior of the complete EEG recordings, we miss moment-to moment fluctuations in functional connectivity that might be informative about the brain states. Therefore, the connectivity matrices of time-dependent multiplex network were computed using a sliding time window technique. 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
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. Previous studies have shown that the choice of EEG reference can affect functional connectivity estimation and the reference electrode standardization technique is proved to be a better choice (Yao, 2001; Lei and Liao, 2017). Montague et al.[17] note that the almost “unreasonable effectiveness of psychotropic medication” has somewhat stymied progress in this field, and advocate for a large-scale “computational phenotyping” of psychiatric patients. Neuroimaging studies of large numbers of these patients could yield brain activation markers for specific psychiatric illnesses, and also aid in the development of therapeutics and animal models. While a true baseline of brain function in psychiatric patients is near-impossible to obtain, reference values can still be measured by comparing images gathered from patients before and after treatment. Where ki is the degree of node i in the corresponding binary network and wij is the link weight between nodes i and j.

Though functional integration frequently relies on anatomic knowledge of the connections between brain areas, the emphasis is on how large clusters of neurons – numbering in the thousands or millions – fire together under various stimuli. The large datasets required for such a whole-scale picture of brain function have motivated the development of several novel and general methods for the statistical analysis of interdependence, such as dynamic causal modelling and statistical linear parametric mapping. These datasets are typically gathered in human subjects by non-invasive methods such as EEG/MEG, fMRI, or PET. 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.
This result is in line with a recent MEG study reporting the disruption of specific occipital hub regions in AD. During the progression of disease, the patients may exhibit decreased hub centrality or number of hubs (Yu https://www.globalcloudteam.com/ et al., 2017). Alternatively, owing to the loss of original hubs, some non-hub areas may become relatively more important to maintain the information flow within or across frequency bands and even become new hubs.

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.

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In contrast, recent neuroimaging studies have shown that the cognitive deficits in AD is related to pathological changes in large-scale functional or structural networks (Dickerson and Sperling, 2005; Greicius, 2008; Sperling et al., 2009; Pievani et al., 2011). Therefore, the investigation of brain networks seems a promising method to study AD pathology. In the past few years, growing attention has been paid to the building of connectivity “neuromarkers” for AD (Toussaint et al., 2012; Franzmeier et al., 2016; Song et al., 2019).
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.