Communities for our graph were detected with the modularity optimization method of Newman . The modularity, or Q, of a graph is a quantitative measure of the number of edges found within communities versus the number predicted in a random graph with equivalent degree distribution. A positive Q indicates that the number of intra-community edges exceeds those predicted statistically. A wide range of Q may be found for a graph, depending on how nodes are assigned to communities. The set of node assignments that returns the highest Q is the optimal community structure sought by the modularity optimization algorithm, which follows a recursive two-step process. First, a modularity matrix similar to a Laplacian is constructed from the nodes in question, comparing observed versus expected edges. If this matrix has a positive eigenvalue, the eigenvector of the largest eigenvalue is used to split the nodes into two subgraphs, and Q is calculated. Second, nodes are swapped individually between the two subgraphs to see if an increase in Q can be found. Once a maximal Q is found from these swaps, the process is repeated on the subgraphs. At any point in this process, if the matrix has no positive eigenvalues, or if a proposed split does not increase Q, the subgraph is set aside, and defines a community. To detect communities in our networks over a range of ages, we used the sliding boxcar group average correlation matrices described above in ‘‘Generation of average group correlation matrices across development.’’ With weights retained, the modularity optimization algorithm was applied to each matrix along the sliding boxcar. A range of thresholds was explored to define connections for these calculations (see Figure 4 and Figure S1). Any particular threshold did not change the conclusions presented in the main manuscript. A threshold of 0.10 was chosen to display in the main manuscript because it balances two principles: (1) eliminating a multitude of weak correlations, which may obscure more physiologically relevant correlations, and (2) retaining high graph connectedness, so that communities arise from partitioning and not thresholding. Graph connectedness captures the extent of nodes fragmented from the main graph due to increasing thresholds. It is defined for a graph of N nodes as the mean of an NxN matrix, where cell i,j is 1 if a path exists between node i and node j (self-connections are allowed), and is 0 otherwise. A graph in which all nodes can reach each other has 100% graph connectedness, whereas a fragmented network in which some nodes cannot reach the rest has a lower connectedness. The modularity optimization analysis returned a set of community assignments for the nodes, as well as the Q of the graph with those assignments. The group assignments for the nodes were converted to colors and are displayed in Figure 4. The
In this study, we used a graph theoretical approach which has been widely used for characterizing brain network architectures [29,30] to compare the topological properties of the brainfunctionalnetworks involved in explicit and implicit language tasks . In the explicit task, subjects were asked to make a semantic congruency judgment on sentences. In the implicit language task, subjects were asked to make font size judgments during which their attention was not necessarily orientated to semantic processing. We assumed that the brainfunctionalnetworks would fit small-worldness criteria regardless of task- specific stimuli. We also expected that the shared active regions in sentence comprehension during explicit and implicit language tasks would be identified as hubs of the functionalnetworks, and the high local and global efficiency of the network can help us to infer the functional integration and segregation, which are two major organizational principles of the human brain . The explicit language task required elaborated semantic analysis, which included different sub-processes, such as semantic retrieval and semantic integration. As these processes involved widespread regions of the entire brain, the explicit language task may thus emphasize global information transfer and alter the properties of the key regions in sentence comprehension, such as the left inferior frontal gyrus (IFG).
Representing brain morphology as a network has the advantage that the regional morphol- ogy of ‘isolated’ structures can be described statistically based on graph theory. However, very few studies have investigated brain morphology from the holistic perspective of com- plex networks, particularly in individual brains. We proposed a new network framework for individual brain morphology. Technically, in the new network, nodes are defined as regions based on a brain atlas, and edges are estimated using our newly-developed inter-regional relation measure based on regional morphological distributions. This implementation allows nodes in the brain network to be functionally/anatomically homogeneous but different with respect to shape and size. We first demonstrated the new network framework in a healthy sample. Thereafter, we studied the graph-theoretical properties of the networks obtained and compared the results with previous morphological, anatomical, and functional net- works. The robustness of the method was assessed via measurement of the reliability of the network metrics using a test-retest dataset. Finally, to illustrate potential applications, the networks were used to measure age-related changes in commonly used network met- rics. Results suggest that the proposed method could provide a concise description of brainorganization at a network level and be used to investigate interindividual variability in brain morphology from the perspective of complex networks. Furthermore, the method could open a new window into modeling the complexly distributedbrain and facilitate the emerg- ing field of human connectomics.
In the current study, we examined the integrity of functionalbrain connectivity in various spectral bands of the electroenceph- alogram (EEG). In addition, we employed graph theoretical network analyses, which allows for a systematic investigation of the network architecture governing neuronal oscillations. Using graph theory, the neural architecture of the brain can be parceled into networks of nodes and links. Nodes are generally referred to as processing units, whereas links represent the (anatomical or functional) connection between the nodes. The organization of nodes and links in a graph is purported to reflect the integrity and efficiency of brainnetworks [21,22]. The clustering coefficient (a measure of local connectedness of a graph) and path length (for unweighted networks: the number of edges in the shortest path between two vertices in a graph) are two indices that reflect the complexity of the graph or brain network , and can be used to classify brain network topology. Human brainnetworks have been shown to resemble the ‘small-world’ properties - characterized by high clustering and short path length that optimize information transfer within the brain network [21,22]. It has been shown that the brain becomes less random and shows increased small-world characteristics with ongoing development [23,24]. Furthermore, it has been shown that shorter normalized path length is associated with higher levels of full-scale IQ [25,26], suggesting that path length is crucial for information processing efficiency within the network.
The interaction between space and topology in brain systems could be driven by energetic and metabolic constraints on network development [3,20,54,73]. Such constraints might also play a role in the fine-grained spatial geometry of white matter fiber tracts, which cross one another at 90 degree angles , thereby potentially minimizing electromagnetic interference. Moreover, such constraints likely have important implications for system function, where short connections are potentially easier to maintain and use than long connections . If such a functional consequence of physical constraints existed, it might partially explain the functional deficits observed in disease states associated with large-scale disconnectivity [59,64,75,76]. However, converse evidence from normal human development indicates that some distributed processing based on long distance connections is necessary for healthy cognitive function . Future work is necessary to better understand the role of physical constraints on brain development and organization.
The neural patterns recorded during a neuroscientific experiment reflect complex interactions between many brain regions, each comprising millions of neurons. However, the measurements themselves are typically abstracted from that underlying structure. For example, functional magnetic resonance imaging (fMRI) datasets comprise a time series of three-dimensional images, where each voxel in an image (roughly) reflects the activity of the brain structure(s)–located at the corresponding point in space–at the time the image was collected. FMRI data often exhibit strong spatial correlations, whereby nearby voxels behave similarly over time as the underlying brain structure modulates its activity. Here we develop topographic factor analysis (TFA), a technique that exploits spatial correlations in fMRI data to recover the underlying structure that the images reflect. Specifically, TFA casts each brain image as a weighted sum of spatial functions. The parameters of those spatial functions, which may be learned by applying TFA to an fMRI dataset, reveal the locations and sizes of the brain structures activated while the data were collected, as well as the interactions between those structures.
In the present study, we hypothesize that functionalnetworks examined using rs-fMRI and structural networks accessed using high angular resolution diffusion imaging (HARDI) can demonstrate age-related compensatory changes in the PFC and posterior regions of the brain at the level of their connections. In particular, we hypothesize that the functional and structural connectivity of the PFC with the posterior regions of the brain increases as age increases. Such age effects could be mediated by the functional and structural connectivity among the posterior regions of the brain. Given well-known knowledge on age-related brain atrophy, we also hy- pothesize that the above age effects may also partially be mediated by brain atrophy. Hence, we employed rs-fMRI, high angular resolution diffusion imaging (HARDI), and graph analysis techniques to examine i) age effects on structural and functional connectivity of the PFC with posterior regions of the brain; ii) mediation effects of structural and functional connectivity among the posterior regions of the brain on age-related changes in structural and functional connectivity of the PFC; iii) mediation effects of brain atrophy on age-related changes in struc- tural and functional connectivity of the PFC. Unlike previous studies where analyses were re- stricted to comparing two age groups (young versus old) [9, 30, 32, 33, 36] or with a small number of subjects across a wide age range [37, 41], we examine age-related connectivity based on 173 subjects aged from 21 to 80 years old (evenly distributed across this age range) to estab- lish a more comprehensive understanding of brain network changes. Moreover, we apply HARDI to examine structural networksto overcome the well-known limitation of DTI, where only one dominant fiber orientation at each location is revealed. Between one and two thirds of the voxels in the human brain white matter are thought to contain multiple fiber bundles cross- ing each other . It has been shown that accurate fiber estimates can be obtained from HARDI data, further validating its usage in brain studies . In addition, we use cortical thickness as an indicator of brain morphological measures in our functional and structural net- work analysis. This is to control for the possible confound of age-related reduction in cortical thickness [44, 45], which has not been accounted for in most of imaging aging studies so far.
During the last years evidence has accumulated suggesting that an improved characterization of time-variant interactions between different regions within the complex network brain can be achieved with graph-theoretical approaches (see [1–6] for an overview). Within this framework a network (or graph) is considered as a set of nodes (or vertices) and a set of links (or edges) connecting the nodes. Functionalbrainnetworks can be derived from direct or indirect measurements of neural activity (e.g., electroencephalogram (EEG), magnetoencephalogram (MEG), or functional magnetic resonance imaging (fMRI) data). The sampled brain regions are usually considered as network nodes, and network links represent interactions between pairs of brain regions that can be assessed by evaluating interdependencies (see [7–11] for an overview) between their neural activities. The resulting connection schemes can then be characterized by network metrics  such as the average shortest path length or the clustering coefficient. The average shortest path length L is the mean number of steps along the shortest paths for all possible pairs of nodes. The clustering coefficient C is the mean of the local clustering coefficients of all nodes and quantifies the tendency of nodes to form local clusters. The local clustering coefficient of a node is the fraction of triangles among all connected triples with the node as their center. Large values of both L and C are characteristic for an ordered, lattice-like structure; low values of L
Graph theoretical analysis of brainnetworks based on resting-state functional MRI (R-fMRI) has attracted a great deal of attention in recent years. These analyses often involve the selection of correlation metrics and specific preprocessing steps. However, the influence of these factors on the topological properties of functionalbrainnetworks has not been systematically examined. Here, we investigated the influences of correlation metric choice (Pearson’s correlation versus partial correlation), global signal presence (regressed or not) and frequency band selection [slow-5 (0.01–0.027 Hz) versus slow-4 (0.027–0.073 Hz)] on the topological properties of both binary and weighted brainnetworks derived from them, and we employed test-retest (TRT) analyses for further guidance on how to choose the ‘‘best’’ network modeling strategy from the reliability perspective. Our results show significant differences in global network metrics associated with both correlation metrics and global signals. Analysis of nodal degree revealed differing hub distributions for brainnetworks derived from Pearson’s correlation versus partial correlation. TRT analysis revealed that the reliability of both global and local topological properties are modulated by correlation metrics and the global signal, with the highest reliability observed for Pearson’s-correlation-based brainnetworks without global signal removal (WOGR-PEAR). The nodal reliability exhibited a spatially heterogeneous distribution wherein regions in association and limbic/paralimbic cortices showed moderate TRT reliability in Pearson’s-correlation-based brainnetworks. Moreover, we found that there were significant frequency-related differences in topological properties of WOGR-PEAR networks, and brainnetworks derived in the 0.027–0.073 Hz band exhibited greater reliability than those in the 0.01–0.027 Hz band. Taken together, our results provide direct evidence regarding the influences of correlation metrics and specific preprocessing choices on both the global and nodal topological properties of functionalbrainnetworks. This study also has important implications for how to choose reliable analytical schemes in brain network studies.
Functional connectivity MRI was used to analyze network properties across the human brain introducing spatial distance information. We discovered that mapping regions based on whether they exhibit preferentially local versus preferentially distant functional connectivity at rest easily separates early sensorimotor, heteromodal association cortices and core regions of the default mode network. This observation reveals a parsimonious property of cortical network architecture that divides processing between many parallel systems characterized by extensive local processing and transmodal regions that serve as hubs connecting these local systems. As a practical application of our approach, metrics of connectivity profiles that reflect local and distributed connectivity can be made rapidly in individual participants. These metrics may thus have value for exploring individual differences both in relation to genetics and also in developmental neuropsychiatric disorders where atypical connec- tivity profiles may be present. More broadly, the observation that connectivity hubs fall within regions of estimated cortical expansion between monkey and humans , and also regions of late child development , reinforces the hypothesis that association areas make an important contribution to higher-order cognitive functions that are especially well developed in humans.
brain function. Along these lines several reports have proposed that phase synchronization via intrinsic activity of specific neural assemblies or networks is important for coordinating segregated and distributed neural processes. For example, Varela et al.  point out that terms such as bottom-up and top-down are only heuristics ‘‘for what is in reality a large-scale network that integrates both incoming and endogenous activity.’’ They continue, ‘‘it is precisely at this level where phase synchronization is crucial as a mechanism for large- scale integration.’’ With this in mind, the rich club nodes and the integration across systems of the structural networks potentially highlights the ‘‘highways’’ at which functional integration of this type might occur during specified task demands; however, because participants are ‘‘at rest’’ (not performing an explicit task here), the synchronization across these highways may not be observed. Such a view is consistent with recent work highlighting the dynamic task-dependent reorganization of multiple large-scale cognitive networks [45,46]. Additional work across various task conditions will be able to further evaluate the notion of cross-systems
Studies in anatomical brain connectivity discovered that small- world network architectures are a distinctive trait in animals [19,21,40], including humans [10,13,41], yet with different degree of brain development. The complementary observation that brain pathologies like epilepsy  and schizophrenia  show small- world network disruptions provides further support to the potential interpretive and explanatory strength of small-word topology. It should be noted that the methodological approaches used to study the functional connectivity at macroscopic and microscopic levels are slightly different. Studies with fMRI estimate functional interactions among brain areas comparing the BOLD signal of each area to a seed region. Scientists usually refer to these effects as functional connectivity [2,10,13]. In this work, instead, we studied networks built from the extracted functional connections comput- ed comparing the electrical activity of all possible neuron couples . Despite the technical incongruences and focusing on neuronal functional connections and the underlying topology, a number of meaningful studies found an intrinsic small-world topology in single visual areas of primates [15,17,19,20,22,23] and in neuronal cultures . These elegant approaches gave access to the richness of the localfunctional connection graphs scaled at the neuronal level. However, none of these studies provided a description of an extended connectivity, involving different neuronal populations gathered in close proximity or located in distant brain regions.
complexity algorithm and with a graph of vertices more than 20 in number, to find a solution for the minimum VCS requires a huge processing power and takes unfeasibly long processing time. Therefore, when such problems are in hand, employing approximation algorithms which present fast and close-to-ideal results is a considerably feasible choice. Approximation algorithms have polynomial time complexities and hence they generate the required results in polynomial time. But these algorithms do not put forward the best results; they approximate the best result which can be considered as an optimal result. By a centralized algorithm, the approximation ratio for a minimum VCS is at least 1.36. The best upper bound known is 2 − (1/ log 2 (n)) [11, 12, 13] .
of 20 g of ‘dulce de leche’. Ot appears that the quantity of FCO and FCPD (1 g/L) applied to the ‘dulce de leche’ was enough to promote beneficial effects on the composition of the product, enabling improvement in the nutritional quality even in foods with high energy demand such as ‘dulce de leche’. Regarding the colour parameters (Table 4), the treatments did not differ (p < 0.05) in L*, a*, and b*, featuring a tint in the region between red (a* +) and yellow (b*+) with values of the hue angle situated between 66.02 and 67.24 hue. Note that the ‘dulce de leche’ showed a dark colour (L*<50) and values of C* between 25.97 and 31.01, demonstrating a more intense colour. The treatments with chia flour did not differ significantly among themselves (p < 0.05) for the parameter ΔE*, and when compared to treatments with AM the colour difference was noticeable; colour distinctions were also identified during the sensory analysis. Evaluating the low luminosity, the slope of the hue angle, and the chromaticity of a* and b* positive, it can be assumed that the combination of these parameters resulted in ‘dulce de leche’ with a brown colour, characteristic of this product, due to reactions during cooking, enhanced by the addition of sodium bicarbonate.
A factorial categorical design totalling six treatments was applied to investigate the influence of the substitution of corn starch with whole and partially defatted chia flour under the technical characteristics (centesimal composition, instrumental analyses, and sensory evaluation) and nutritional disorders (composition of fatty acids and index of the nutritional quality of the lipid fraction) of ‘dulce de leche’ concentrated to 72 and 78 °B. The treatments with chia flour concentrated to 72 °B showed higher moisture content and lower compression force, and when the concentration range increased to 78 °B, the levels of total lipids amounted up to 1.40 times when compared to treatment with corn starch. The polyunsaturated fatty acids, particularly omega-3 and omega-6 levels, were higher in treatments with chia flour on both tracks of concentration, allowing a reduction in the atherogenic index and thrombogenic index effects and the n-6/n-3 ratio. The treatments of ‘dulce de leche’ with a lower concentration of soluble solids obtained greater acceptance and consumer purchase intention. The application of whole chia flour in small proportions and in the concentration of 72 °B was the most appropriate under the studied conditions, showing improvement in the nutritional quality and with good technical aspects of candy made with goat milk.
The main design of the Slsnj, which is a simple finite state machine. As shown in figure 1, a node running Slsnj is in one of four states at any time: (i) Sensor not estimated, (ii) Sensor estimated, (iii) estimated Anchor,and (iv) improve the accuracy. Transitions between the states are triggered by events. After the Slsnj protocol is initiated, the node enters the Sensor not estimated state,Whenever the node receives a broadcasting ProbePacket packet, the node enters the Sensor not estimated state and uses this packet to estimate its postion,after this stage of estimation the node switches to another state is depending on the value of the estimation error found,if espilon<threshold the node enters in estimated Anchor state else it enters in Sensor estimated state .In the latter two states a node is still waiting of probpacket packet from anchor or estimated Anchor nodes to enter in improve the accuracy state and improve its accuracy.when there will be no more ProbePacket, the node switches to the state final and considered as estimated with an error of precison. An example is illustrated in figure 2. X receives positions of anchors
It is hypothesized that plasticity is guided by the particular lesional growth pattern . A recent computational modeling study allowing both growth- and synchronization-dependent plasticity showed that acute lesioning of functionalnetworks leads to increased local clustering levels . Although the model only considered an acute lesion which limits comparability with our study, this is consistent with the increased clustering that we found in LGG patients. However, we found no network differences between HGG patients and healthy controls. A possible explana- tion is that it might take time before plasticity effects become evident on a global scale, and HGG patients tended to have shorter time between first symptoms and MEG recordings . In the model of Stam and others, however, increased path lengths and decreased modularity were particularly found directly after emergence of the lesion, subsequently normalizing over time . Alternatively, our results may also have been affected by epilepsy characteristics and use of AEDs [15,16,17]. Patient groups in our study were relatively small to analyze within group correlations between epilepsy and network characteristics, but we did find a correlation between network synchronizability and seizure fre- quency in LGG patients. It would be interesting to compare glioma patients with and without epilepsy, and find possible differences in the functionalnetworks of these patients. However, since we found no significant differences between LGG and HGG patients regarding epilepsy duration, seizure frequency and AED use, we consider it unlikely these characteristics would explain differences between these groups.
Gradient echo sequences are of special interest in the measurement of T 2 ∗ ef- fects since they are extremely sensitive to this relaxation rate. As stated in section 2.1.2, T 2 ∗ is strongly correlated with field inhomogeneities and there- fore, by using acquisition sequences sensitive to this parameter it is possi- ble to map local field variations. Haemoglobin (Hb) is an oxygen carrying molecule present in red blood cells, whose magnetic properties depend on the presence or absence of oxygen. Oxyhaemoglobin (oHb) is diamagnetic and Deoxyhaemoglobin (dHb) is paramagnetic, therefore local magnetic proper- ties are modified by the oxygenation state allowing Susceptibility Weighted (SW) imaging to make use of gradient echo sequences to map local magni- tude and phase changes that naturally occur in the human brain. Thanks to dHb presence in venous blood vessels and bleeds, SW imaging is able to produce reliable venographic images of the human brain as well as detecting micro-bleeds inside it.
To the best of our knowledge, no study has been done on the EC of brainnetworks in MCI/aMCI patients. In this work, we address the limitations in previous studies of resting state brainnetworks in MCI patients. First, we examined the connectivity patterns within and between four important brainnetworks, including the DMN [30–31], the dorsal attention network (DAN) , the fronto-parietal control network (FPCN)  and the HCMN . These functionalbrainnetworks have been confirmed by using resting state functional connectivity, as measured by Pearson’s correlation in low frequency fluctuations (LFF) ( ,0.1 Hz) of the blood oxygen level-dependent (BOLD) signal. Of particular interest are DMN and DAN, since the former is engaged by internally directed cognition and the latter by externally directed cognition, and hence are anti-correlated [34– 35]. It has been hypothesized that FPCN mediates the interaction between DMN and DAN [33,36], given the evidence that it is anatomically juxtaposed between DMN and DAN. As aMCI patients have evident memory impairment, it is of direct interest to examine the connectivity with HCMN and the interactions between HCMN and the other three basic networks. We will define the functional regions of interest (ROI) of four networks based on coordinates in previous published literatures to obtain time series specific to each ROI, unlike previous ICA-based studies which obtained a single time series for the entire network. This allowed us to examine the intra- and inter- networks connectivity without losing spatial specificity.
To create new products means to produce more waste; if more waste is created, more space it needs to be thrown. It’s clear that this is a textile process that takes advantage of natural resources to satisfy human needs. As Almeida (2002) stated, this is a scenario where human beings sees itself away from nature, thinking about it only as means for production. When human beings exclude themselves from the ecosystem - the system of all living beings - human beings create serious environmental issues, using so much of natural resources that nature can run out of it. In the past, the planet was one cyclic and unlimited biosphere where each living being would, at the same time, use and generate a resource. In a specific way, the fashion market can be an example of that worrisome reality (HOSKINS, 2014; GIUDICE, LA ROSA E RISITANO, 2006).