Local Connectivity Properties Research Articles

High-dimensional aerodynamic data modeling using a machine learning method based on a convolutional neural network

Modeling high-dimensional aerodynamic data presents a significant challenge in aero-loads prediction, aerodynamic shape optimization, flight control, and simulation. This article develops a machine learning approach based on a convolutional neural network (CNN) to address this problem. A CNN can implicitly distill features underlying the data. The number of parameters to be trained can be significantly reduced because of its local connectivity and parameter-sharing properties, which is favorable for solving high-dimensional problems in which the training cost can be prohibitive. A hypersonic wing similar to the Sanger aerospace plane carrier wing is employed as the test case to demonstrate the CNN-based modeling method. First, the wing is parameterized by the free-form deformation method, and 109 variables incorporating flight status and aerodynamic shape variables are defined as model input. Second, more than 7000 sample points generated by the Latin hypercube sampling method are evaluated by performing computational fluid dynamics simulations using a Reynolds-averaged Navier–Stokes flow solver to obtain an aerodynamic database, and a CNN model is built based on the observed data. Finally, the well-trained CNN model considering both flight status and shape variables is applied to aerodynamic shape optimization to demonstrate its capability to achieve fast optimization at multiple flight statuses.

Fine‐Grained Scene Graph Generation with Overlap Region and Geometrical Center

AbstractScene graph generation refers to the task of identifying the objects and specifically the relationships between the objects from an image. Existing scene graph generation methods generally use the bounding boxes region features of objects to identify the relationships between objects. However, we feel that the overlap region features of two objects may play an important role in fine‐grained relationship identification. In fact, some fine‐grained relationships can only be obtained from the overlap region features of two objects. Therefore, we propose the Multi‐Branch Feature Combination (MFC) module and Overlap Region Transformer (ORT) module to comprehensively obtain the visual features contained in the overlap regions of two objects. Concretely, the MFC module uses deconvolution and multi‐branch dilation convolution to obtain high‐pixels and multi‐receptive field features in the overlap regions. The ORT module uses the vision transformer to obtain the self‐attention of the overlap regions. The joint use of these two modules achieves the mutual complementation of local connectivity properties of convolution and the global connectivity properties of attention. We also design a Geometrical Center Augmented (GCA) module to obtain the relative position information of the geometric centers between two objects, to prevent the problem that only relying on the scale of the overlap region cannot accurately capture the relationship between two objects. Experiments show that our model ORGC (Overlap Region and Geometrical Center), the combination of the MFC module, the ORT module, and the GCA module, can enhance the performance of fine‐grained relation identification. On the Visual Genome dataset, our model outperforms the current state‐of‐the‐art model by 4.4% on the R@50 evaluation metric, reaching a state‐of‐the‐art result of 33.88.

Network Centrality Reveals Dissociable Brain Activity during Response Inhibition in Human Right Ventral Part of Inferior Frontal Cortex

The human right inferior frontal cortex (IFC) plays a critical role in response inhibition. It has also been demonstrated that the IFC is heterogeneous and that the ventral part of the IFC (vIFC) is more critical to inhibition of prepotent response tendency. Recent areal parcellation analyses based on resting-state functional connectivity have revealed that the right vIFC consists of multiple functional areas. In the present study, we characterized the parcellated areas (parcels) in the right vIFC using graph theory analysis, which characterizes local connectivity properties of a brain network by referring to its global structure of functional connectivity. Functional magnetic resonance imaging (MRI) scans were obtained during performance of a stop-signal task and during resting state. The cerebral cortex was parcellated into areas using resting-state functional connectivity. The parcels were then subjected to graph theory analysis to reveal central areas. Two parcels, ventral and dorsal, in the posterior part of the vIFC, exhibited significant brain activity during response inhibition. The ventral parcel exhibited a positive correlation between betweenness centrality and brain activity while the dorsal parcel did not. Correlations were significantly stronger in the ventral parcel. Moreover, the ventral parcel exhibited a negative correlation between brain activity during response inhibition and stop-signal reaction time (SSRT), a behavioral measure used to evaluate stopping performance. These dissociation results suggest that the ventral region in the vIFC plays a more central role in the brain network by increasing brain activity, which may further predict better performance of response inhibition.

Evaluating graph resilience with tensor stack networks: a Keras implementation

In communication networks resilience or structural coherency, namely the ability to maintain total connectivity even after some data links are lost for an indefinite time, is a major design consideration. Evaluating resilience is a computationally challenging task since it often requires examining a prohibitively high number of connections or of node combinations, depending on the structural coherency definition. In order to study resilience, communication systems are treated in an abstract level as graphs where the existence of an edge depends heavily on the local connectivity properties between the two nodes. Once the graph is derived, its resilience is evaluated by a tensor stack network (TSN). TSN is an emerging deep learning classification methodology for big data which can be expressed either as stacked vectors or as matrices, such as images or oversampled data from multiple-input and multiple-output digital communication systems. As their collective name suggests, the architecture of TSNs is based on tensors, namely higher-dimensional vectors, which simulate the simultaneous training of a cluster of ordinary multilayer feedforward neural networks (FFNNs). In the TSN structure the FFNNs are also interconnected and, thus, at certain steps of the training process they learn from the errors of each other. An additional advantage of the TSN training process is that it is regularized, resulting in parsimonious classifiers. The TSNs are trained to evaluate how resilient a graph is, where the real structural strength is assessed through three established resiliency metrics, namely the Estrada index, the odd Estrada index, and the clustering coefficient. Although the approach of modelling the communication system exclusively in structural terms is function oblivious, it can be applied to virtually any type of communication network independently of the underlying technology. The classification achieved by four configurations of TSNs is evaluated through six metrics, including the F1 metric as well as the type I and type II errors, derived from the corresponding contingency tables. Moreover, the effects of sparsifying the synaptic weights resulting from the training process are explored for various thresholds. Results indicate that the proposed method achieves a very high accuracy, while it is considerably faster than the computation of each of the three resilience metrics. Concerning sparsification, after a threshold the accuracy drops, meaning that the TSNs cannot be further sparsified. Thus, their training is very efficient in that respect.

Local structure, connectivity and physical properties of glasses in the B2O3-Bi2O3-La2O3-WO3 system

Glasses of (100 - (x + y))·(0.6B2O3·0.4Bi2O3)·xLa2O3·yWO3, x = 0, 10; y = 0 ÷ 40 mol% were prepared by melt quenching. Density measurements, thermal analysis, UV–vis diffuse reflectance spectroscopy, X-ray photoelectron spectroscopy and theoretical modeling using Density Functional Theory were employed to identify the effect of WO3 content on the structural and physicochemical properties of these glasses. The glass transition temperature and density increase steadily with increasing WO3 content, most probably because of the formation of mixed Bi–O–W and La–O–W crosslinks. The lower band gap energy values show that the introduction of WO3 or La2O3 to 60B2O3·40Bi2O3 glass increases the number of non-bridging oxygen species in the glass structure. The photoelectron analysis aided by theoretical calculations discover that additionally to the tetrahedrally coordinated W ions, most of the existing WO6 octahedral units in glasses with nominal WO3 content below 20 mol% are distorted, leaving practically the tungsten ions in a quasi-tetrahedral coordination. At higher WO3 content (30–40 mol%) the concentration of octahedrally coordinated tungsten atoms dominate strongly over those of tetra- and quasi-tetra-coordinated W ions. Moreover, the comparison with appropriate crystal standards allows offering a complete description of the existing bridging and non-bridging linkages and their most likely O1s binding energies.

Structural brain network fingerprints of focal dystonia.

Background:Focal dystonias are severe and disabling movement disorders of a still unclear origin. The structural brain networks associated with focal dystonia have not been well characterized. Here, we investigated structural brain network fingerprints in patients with blepharospasm (BSP) compared with those with hemifacial spasm (HFS), and healthy controls (HC). The patients were also examined following treatment with botulinum neurotoxin (BoNT).Methods:This study included matched groups of 13 BSP patients, 13 HFS patients, and 13 HC. We measured patients using structural-magnetic resonance imaging (MRI) at baseline and after one month BoNT treatment, at time points of maximal and minimal clinical symptom representation, and HC at baseline. Group regional cross-correlation matrices calculated based on grey matter volume were included in graph-based network analysis. We used these to quantify global network measures of segregation and integration, and also looked at local connectivity properties of different brain regions.Results:The networks in patients with BSP were more segregated than in patients with HFS and HC (p < 0.001). BSP patients had increased connectivity in frontal and temporal cortices, including sensorimotor cortex, and reduced connectivity in the cerebellum, relative to both HFS patients and HC (p < 0.05). Compared with HC, HFS patients showed increased connectivity in temporal and parietal cortices and a decreased connectivity in the frontal cortex (p < 0.05). In BSP patients, the connectivity of the frontal cortex diminished after BoNT treatment (p < 0.05). In contrast, HFS patients showed increased connectivity in the temporal cortex and reduced connectivity in cerebellum after BoNT treatment (p < 0.05).Conclusions:Our results show that BSP patients display alterations in both segregation and integration in the brain at the network level. The regional differences identified in the sensorimotor cortex and cerebellum of these patients may play a role in the pathophysiology of focal dystonia. Moreover, symptomatic reduction of hyperkinesia by BoNT treatment was associated with different brain network fingerprints in both BSP and HFS patients.

Local connectivity of the resting brain connectome in patients with low back-related leg pain: A multiscale frequency-related Kendall's coefficient of concordance and coherence-regional homogeneity study.

Increasing evidence has suggested that central plasticity plays a crucial role in the development and maintenance of (chronic) nonspecific low back pain. However, it is unclear how local or short-distance functional interactions contribute to persisting low back-related leg pain (LBLP) due to a specific condition (i.e., lumbar disc herniation). In particular, the multiscale nature of local connectivity properties in various brain regions is still unclear. Here, we used voxelwise Kendall's coefficient of concordance (KCC) and coherence (Cohe) regional homogeneity (ReHo) in the typical (0.01–0.1 Hz) and five specific frequency (slow-6 to slow-2) bands to analyze individual whole-brain resting-state functional magnetic resonance imaging scans in 25 persistent LBLP patients (duration: 36.7 ± 9.6 months) and 26 healthy control subjects. Between-group differences demonstrated significant alterations in the KCC- and Cohe- ReHo of the right cerebellum posterior lobe, brainstem, left medial prefrontal cortex and bilateral precuneus in LBLP patients in the typical and five specific frequency bands, respectively, along with interactions between disease status and the five specific frequency bands in several regions of the pain matrix and the default-mode network (P < .01, Gaussian random field theory correction). The altered ReHo in the five specific frequency bands was correlated with the duration of pain and two-point discrimination, which were assessed using partial correlational analysis. These results linked the course of disease to the local connectivity properties in specific frequency bands in persisting LBLP. In future studies exploring local connectome association in pain conditions, integrated frequency bands and analytical methods should be considered.

Unaltered intrinsic functional brain architecture in young women with primary dysmenorrhea

Primary dysmenorrhea (PDM), painful menstruation without organic causes, is the most prevalent gynecological problem in women of reproductive age. Dysmenorrhea later in life often co-occurs with many chronic functional pain disorders, and chronic functional pain disorders exhibit altered large-scale connectedness between distributed brain regions. It is unknown whether the young PDM females exhibit alterations in the global and local connectivity properties of brain functional networks. Fifty-seven otherwise healthy young PDM females and 62 age- and education-matched control females participated in the present resting-state functional magnetic resonance imaging study. We used graph theoretical network analysis to investigate the global and regional network metrics and modular structure of the resting-state brain functional networks in young PDM females. The functional network was constructed by the interregional functional connectivity among parcellated brain regions. The global and regional network metrics and modular structure of the resting-state brain functional networks were not altered in young PDM females at our detection threshold (medium to large effect size differences [Cohen’s d ≥ 0.52]). It is plausible that the absence of significant changes in the intrinsic functional brain architecture allows young PDM females to maintain normal psychosocial outcomes during the pain-free follicular phase.

A unified treatment of linked and lean tree-decompositions

There are many results asserting the existence of tree-decompositions of minimal width which still represent local connectivity properties of the underlying graph, perhaps the best known being Thomas' theorem that proves for every graph G the existence of a linked tree-decomposition of width tw(G). We prove a general theorem on the existence of linked and lean tree-decompositions, providing a unifying proof of many known results in the field, as well as implying some new results. In particular we prove that every matroid M admits a lean tree-decomposition of width tw(M), generalizing the result of Thomas.

Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks.

The study of processes evolving on networks has recently become a very popular research field, not only because of the rich mathematical theory that underpins it, but also because of its many possible applications, a number of them in the field of biology. Indeed, molecular signaling pathways, gene regulation, predator-prey interactions and the communication between neurons in the brain can be seen as examples of networks with complex dynamics. The properties of such dynamics depend largely on the topology of the underlying network graph. In this work, we want to answer the following question: Knowing network connectivity, what can be said about the level of third-order correlations that will characterize the network dynamics? We consider a linear point process as a model for pulse-coded, or spiking activity in a neuronal network. Using recent results from theory of such processes, we study third-order correlations between spike trains in such a system and explain which features of the network graph (i.e. which topological motifs) are responsible for their emergence. Comparing two different models of network topology—random networks of Erdős-Rényi type and networks with highly interconnected hubs—we find that, in random networks, the average measure of third-order correlations does not depend on the local connectivity properties, but rather on global parameters, such as the connection probability. This, however, ceases to be the case in networks with a geometric out-degree distribution, where topological specificities have a strong impact on average correlations.

Connectivity Scaling Laws in Wireless Networks

We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas exploited for diversity coding and/or beamforming at each node. We demonstrate that the local probability of connectivity scales like $\mathcal{O}(z^\mathcal C)$ in these parameters, where $\mathcal C$ is the ratio of the dimension of the network domain to the path loss exponent, thus enabling efficient boundary effect mitigation and network topology control.

A Path-Based Distance for Street Map Comparison

Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ. However, the majority of current graph comparison algorithms are based on structural properties of graphs, such as their degree distribution or their local connectivity properties, and do not consider their spatial embedding. This ignores a key property of road networks since the similarity of travel over two road networks is intimately tied to the specific spatial embedding. Likewise, many current algorithms specific to street map comparison either do not provide quality guarantees or focus on spatial embeddings only. Motivated by road network comparison, we propose a new path-based distance measure between two planar geometric graphs that is based on comparing sets of travel paths generated over the graphs. Surprisingly, we are able to show that using paths of bounded link-length, we can capture global structural and spatial differences between the graphs. We show how to utilize our distance measure as a local signature in order to identify and visualize portions of high similarity in the maps. Finally, we present an experimental evaluation of our distance measure and its local signature on street map data from Berlin, Germany and Athens, Greece.

Integration of network topological and connectivity properties for neuroimaging classification.

Rapid advances in neuroimaging techniques have provided an efficient and noninvasive way for exploring the structural and functional connectivity of the human brain. Quantitative measurement of abnormality of brain connectivity in patients with neurodegenerative diseases, such as mild cognitive impairment (MCI) and Alzheimer's disease (AD), have also been widely reported, especially at a group level. Recently, machine learning techniques have been applied to the study of AD and MCI, i.e., to identify the individuals with AD/MCI from the healthy controls (HCs). However, most existing methods focus on using only a single property of a connectivity network, although multiple network properties, such as local connectivity and global topological properties, can potentially be used. In this paper, by employing multikernel based approach, we propose a novel connectivity based framework to integrate multiple properties of connectivity network for improving the classification performance. Specifically, two different types of kernels (i.e., vector-based kernel and graph kernel) are used to quantify two different yet complementary properties of the network, i.e., local connectivity and global topological properties. Then, multikernel learning (MKL) technique is adopted to fuse these heterogeneous kernels for neuroimaging classification. We test the performance of our proposed method on two different data sets. First, we test it on the functional connectivity networks of 12 MCI and 25 HC subjects. The results show that our method achieves significant performance improvement over those using only one type of network property. Specifically, our method achieves a classification accuracy of 91.9%, which is 10.8% better than those by single network-property-based methods. Then, we test our method for gender classification on a large set of functional connectivity networks with 133 infants scanned at birth, 1 year, and 2 years, also demonstrating very promising results.

Test–retest reliability of fMRI-based graph theoretical properties during working memory, emotion processing, and resting state

The investigation of the brain connectome with functional magnetic resonance imaging (fMRI) and graph theory analyses has recently gained much popularity, but little is known about the robustness of these properties, in particular those derived from active fMRI tasks. Here, we studied the test–retest reliability of brain graphs calculated from 26 healthy participants with three established fMRI experiments (n-back working memory, emotional face-matching, resting state) and two parcellation schemes for node definition (AAL atlas, functional atlas proposed by Power et al.). We compared the intra-class correlation coefficients (ICCs) of five different data processing strategies and demonstrated a superior reliability of task-regression methods with condition-specific regressors. The between-task comparison revealed significantly higher ICCs for resting state relative to the active tasks, and a superiority of the n-back task relative to the face-matching task for global and local network properties. While the mean ICCs were typically lower for the active tasks, overall fair to good reliabilities were detected for global and local connectivity properties, and for the n-back task with both atlases, smallworldness. For all three tasks and atlases, low mean ICCs were seen for the local network properties. However, node-specific good reliabilities were detected for node degree in regions known to be critical for the challenged functions (resting-state: default-mode network nodes, n-back: fronto-parietal nodes, face-matching: limbic nodes). Between-atlas comparison demonstrated significantly higher reliabilities for the functional parcellations for global and local network properties. Our findings can inform the choice of processing strategies, brain atlases and outcome properties for fMRI studies using active tasks, graph theory methods, and within-subject designs, in particular future pharmaco-fMRI studies.

Network Centrality in the Human Functional Connectome

The network architecture of functional connectivity within the human brain connectome is poorly understood at the voxel level. Here, using resting state functional magnetic resonance imaging data from 1003 healthy adults, we investigate a broad array of network centrality measures to provide novel insights into connectivity within the whole-brain functional network (i.e., the functional connectome). We first assemble and visualize the voxel-wise (4 mm) functional connectome as a functional network. We then demonstrate that each centrality measure captures different aspects of connectivity, highlighting the importance of considering both global and local connectivity properties of the functional connectome. Beyond "detecting functional hubs," we treat centrality as measures of functional connectivity within the brain connectome and demonstrate their reliability and phenotypic correlates (i.e., age and sex). Specifically, our analyses reveal age-related decreases in degree centrality, but not eigenvector centrality, within precuneus and posterior cingulate regions. This implies that while local or (direct) connectivity decreases with age, connections with hub-like regions within the brain remain stable with age at a global level. In sum, these findings demonstrate the nonredundancy of various centrality measures and raise questions regarding their underlying physiological mechanisms that may be relevant to the study of neurodegenerative and psychiatric disorders.

Effective Versions of Local Connectivity Properties

We investigate, and prove equivalent, effective versions of local connectivity and uniformly local arcwise connectivity for connected and computably compact subspaces of Euclidean space. We also prove that Euclidean continua that are computably compact and effectively locally connected are computably arcwise connected.

Conditional Mutual Information Maps as Descriptors of Net Connectivity Levels in the Brain

There is a growing interest in finding ways to summarize the local connectivity properties of the brain through single brain maps. Here we propose a method based on the conditional mutual information (CMI) in the frequency domain. CMI maps quantify the amount of non-redundant covariability between each site and all others in the rest of the brain, partialling out the joint variability due to gross physiological noise. Average maps from a sample of 45 healthy individuals scanned in the resting state show a clear and symmetric pattern of connectivity maxima in several regions of cortex, including prefrontal, orbitofrontal, lateral–parietal, and midline default mode network components; and in subcortical nuclei, including the amygdala, thalamus, and basal ganglia. Such cortical and subcortical hotspots of functional connectivity were more clearly evident at lower frequencies (0.02–0.1 Hz) than at higher frequencies (0.1–0.2 Hz) of endogenous oscillation. CMI mapping can also be easily applied to perform group analyses. This is exemplified by exploring effects of normal aging on CMI in a sample of healthy controls and by investigating correlations between CMI and positive psychotic symptom scores in a sample of 40 schizophrenic patients. Both the normative aging and schizophrenia studies reveal functional connectivity trends that converge with reported findings from other studies, thus giving further support to the validity of the proposed method.

On the anomalous behaviour of a class of locality statistics

A scan statistic methodology for detecting anomalies has been developed for application to graphs, where “anomalies” are equated with vertices that exhibit distinctive local connectivity properties. We present an “anomaly graph” construction that illustrates the capabilities of these scan statistics via the behaviour of their associated locality statistics on our anomaly graphs.

Emergence of scale-free networks from local connectivity and communication trade-offs

We suggest a mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the addition of edges. A new edge is added between two nodes depending on the trade-off between a gain and a cost function of local connectivity and communication properties. We report on simulation results that indicate the appearance of power-law distributions of node degrees for selected parameter combinations.

Various types of local connectedness in n-fold hyperspaces

Let X be a continuum. The n-fold hyperspace C n ( X ) , n < ∞ , is the space of all nonempty compact subsets of X with the Hausdorff metric. Four types of local connectivity at points of C n ( X ) are investigated: connected im kleinen, locally connected, arcwise connected im kleinen and locally arcwise connected. Characterizations, as well as necessary or sufficient conditions, are obtained for C n ( X ) to have one or another of the local connectivity properties at a given point. Several results involve the property of Kelley or C * -smoothness. Some new results are obtained for C ( X ) , the space of subcontinua of X. A class of continua X is given for which C n ( X ) is connected im kleinen only at subcontinua of X and for which any two such subcontinua must intersect.