Network Geometry Research Articles

Geometrical congruence, greedy navigability and myopic transfer in complex networks and brain connectomes

We introduce in network geometry a measure of geometrical congruence (GC) to evaluate the extent a network topology follows an underlying geometry. This requires finding all topological shortest-paths for each nonadjacent node pair in the network: a nontrivial computational task. Hence, we propose an optimized algorithm that reduces 26 years of worst scenario computation to one week parallel computing. Analysing artificial networks with patent geometry we discover that, different from current belief, hyperbolic networks do not show in general high GC and efficient greedy navigability (GN) with respect to the geodesics. The myopic transfer which rules GN works best only when degree-distribution power-law exponent is strictly close to two. Analysing real networks—whose geometry is often latent—GC overcomes GN as marker to differentiate phenotypical states in macroscale structural-MRI brain connectomes, suggesting connectomes might have a latent neurobiological geometry accounting for more information than the visible tridimensional Euclidean.

3D natural fracture model of shale reservoir based on petrophysical characterization

The existence and distribution of natural fractures in shale reservoirs is of great significance to shale gas exploitation. A 3D fracture spatial distribution model with varying reservoir burial depth and regional tectonicsin southeastern Chongqing is constructed based on an enhanced DFN modeling method. Fracture volume density (P32) is calculated by petrophysical test and verified from test wells. The geometric parameters of fractures (length, occurrence, opening) are clustered by regional tectonics. Uncertainties are considered by a stochastic description of the fracture network geometry, utilizing Monte Carlo simulation techniques. The application of the model in seven wells and the quantitative analysis of the relationship between fracture density and burial depth allow the modeling to be extended to deep and ultra-deep reservoirs. Fracture models with reservoirs buried depth over 3000 m are predicted and analyzed. For the various input parameters, the influence of model size and fracture shape on model reliability is analyzed. The establishment of fracture model can effectively quantitatively characterize the reservoir fracture distribution at different burial depths, and its efficient implementation in finite element software can provide support for shale gas mining engineering.

A Comparative Analysis of Convolutional Neural Networks for Trash Classification

In the era of the twenty-first century, automation is the biggest fi eld of research. Although several works have been done successfully, there is still so much to do. Increasing trash could be the biggest threat to a better human life in the future. To automate the task, machines need to understand the type of trash to be recycled or separate similar trash for recycling. For this process, the perfect classi cation of trash plays a vital role in making a better life and a cleaner world. There are so many popular convolutional neural network (CNN) models for image classi cation. In this work, we examine and analyze the outcomes of several Residual Network(ResNet) and Visual Geometry Group (VGG) CNN models on a trash dataset. Our main investigation is the accuracy evaluation for different VGG and ResNet models where the training dataset, test dataset, number of epochs, and batch size are the same for all the models. Finally, we compare VGG and ResNet models with each other. We have got the peak accuracy for ResNet152 among all ResNet models and the peak accuracy on VGG16 among all VGG models. And we have got the maximum accuracy on ResNet152 among all the ResNet and VGG models which is about 94%. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 8, Dec 2021 P 17-23

Detecting hyperbolic geometry in networks: Why triangles are not enough.

In the past decade, geometric network models have received vast attention in the literature. These models formalize the natural idea that similar vertices are likely to connect. Because of that, these models are able to adequately capture many common structural properties of real-world networks, such as scale invariance and high clustering. Indeed, many real-world networks can be accurately modeled by positioning vertices of a network graph in hyperbolic spaces. Nevertheless, if one observes only the network connections, the presence of geometry is not always evident. Currently, triangle counts and clustering coefficients are the standard statistics to signal the presence of geometry. In this paper we show that triangle counts or clustering coefficients are insufficient because they fail to detect geometry induced by hyperbolic spaces. We, therefore, introduce a differerent statistic, weighted triangles, which weighs triangles based on their evidence for geometry. We show analytically, as well as on synthetic and real-world data, that weighted triangles are a powerful statistic to detect hyperbolic geometry in networks.

User Association in a Heterogeneous Vehicular Network With Roadside Units and Vehicle Relays

This letter investigates the behavior of users in a vehicular network where there are two types of transmitters—roadside units (RSUs) and vehicle relays. We address the unique network geometry of such a network by adapting the Cox point process, the double slope path loss, and the strongest average power user association. We derive the probability that users are associated with either RSUs or relays. The association formula explicitly quantifies the change of user association behavior when the heterogeneous vehicular network has two types of transmitters distinctive in their transmit powers and densities. Leveraging this letter, one can explore the potential and benefits of heterogeneous vehicular networks with RSUs and vehicle relays.

Feasibility of Vascular Parameter Estimation for Assessing Hypertensive Pregnancy Disorders.

Hypertensive pregnancy disorders (HPDs), such as pre-eclampsia, are leading sources of both maternal and fetal morbidity in pregnancy. Noninvasive imaging, such as ultrasound (US) and magnetic resonance imaging (MRI), is an important tool for predicting and monitoring these high risk pregnancies. While imaging can measure hemodynamic parameters, such as uterine artery pulsatility and resistivity indices (PI and RI), the interpretation of such metrics for disease assessment relies on ad hoc standards, which provide limited insight to the physical mechanisms underlying the emergence of hypertensive pregnancy disorders. To provide meaningful interpretation of measured hemodynamic data in patients, advances in computational fluid dynamics can be brought to bear. In this work, we develop a patient-specific computational framework that combines Bayesian inference with a reduced-order fluid dynamics model to infer parameters, such as vascular resistance, compliance, and vessel cross-sectional area, known to be related to the development of hypertension. The proposed framework enables the prediction of hemodynamic quantities of interest, such as pressure and velocity, directly from sparse and noisy MRI measurements. We illustrate the effectiveness of this approach in two systemic arterial network geometries: an aorta with branching carotid artery and a maternal pelvic arterial network. For both cases, the model can reconstruct the provided measurements and infer parameters of interest. In the case of the maternal pelvic arteries, the model can make a distinction between the pregnancies destined to develop hypertension and those that remain normotensive, expressed through the value range of the predicted absolute pressure.

Improving Map Matching of Floating Car Data with Artificial Intelligence Techniques

Map matching is a crucial data processing task for transferring measurements from the dynamic sensor location to the relevant road segment. It is especially important when estimating road network speed by using probe vehicles (floating car data) as speed measurement sensors. Most common approaches rely on finding the closet road segment, but road network geometry (e.g., dense areas, two-way streets, and superposition of road segments due to different heights) and inaccuracy in the GNSS location (up to decades of meters in urban areas) can wrongly allocate up to 30% of the measurements. More advanced methods rely on taking the topology of the network into account, significantly improving the accuracy at a higher computational cost, especially when the accuracy of the GNSS location is low. In order to both improve the accuracy of the “closet road segment” methods and reduce the processing time of the topology-based methods, the data can be pre-processed using AI techniques to reduce noise created by the inaccuracy of the GNSS location and improve the overall accuracy of the map-matching task. This paper applies AI to correct GNSS locations and improve the map-matching results, achieving a matching accuracy of 76%. The proposed methodology is demonstrated to the floating car data generated by a fleet of 1200 taxi vehicles in Thessaloniki used to estimate road network speed in real time for information services and for supporting traffic management in the city.

Micro-scale functional modules in the human temporal lobe

The sensory cortices of many mammals are often organized into modules in the form of cortical columns, yet whether modular organization at this spatial scale is a general property of the human neocortex is unknown. The strongest evidence for modularity arises when measures of connectivity, structure, and function converge. Here we use microelectrode recordings in humans to examine functional connectivity and neuronal spiking responses in order to assess modularity in submillimeter scale networks. We find that the human temporal lobe consists of temporally persistent spatially compact modules approximately 1.3mm in diameter. Functionally, the information coded by single neurons during an image categorization task is more similar for neurons belonging to the same module than for neurons from different modules. The geometry, connectivity, and spiking responses of these local cortical networks provide converging evidence that the human temporal lobe is organized into functional modules at the micro scale.

Changes in the geometry and robustness of diffusion tensor imaging networks: Secondary analysis from a randomized controlled trial of young autistic children receiving an umbilical cord blood infusion.

Diffusion tensor imaging (DTI) has been used as an outcome measure in clinical trials for several psychiatric disorders but has rarely been explored in autism clinical trials. This is despite a large body of research suggesting altered white matter structure in autistic individuals. The current study is a secondary analysis of changes in white matter connectivity from a double-blind placebo-control trial of a single intravenous cord blood infusion in 2-7-year-old autistic children (1). Both clinical assessments and DTI were collected at baseline and 6 months after infusion. This study used two measures of white matter connectivity: change in node-to-node connectivity as measured through DTI streamlines and a novel measure of feedback network connectivity, Ollivier-Ricci curvature (ORC). ORC is a network measure which considers both local and global connectivity to assess the robustness of any given pathway. Using both the streamline and ORC analyses, we found reorganization of white matter pathways in predominantly frontal and temporal brain networks in autistic children who received umbilical cord blood treatment versus those who received a placebo. By looking at changes in network robustness, this study examined not only the direct, physical changes in connectivity, but changes with respect to the whole brain network. Together, these results suggest the use of DTI and ORC should be further explored as a potential biomarker in future autism clinical trials. These results, however, should not be interpreted as evidence for the efficacy of cord blood for improving clinical outcomes in autism. This paper presents a secondary analysis using data from a clinical trial that was prospectively registered with ClinicalTrials.gov(NCT02847182).

Social network geometry, linguistic ideologies, and identity negotiation among Latinx English speakers in New Orleans

AbstractThis article presents an analysis of the role of social networks in shaping patterns of /æ/ realization among Latinxs in Post‐Katrina New Orleans. Social network metrics are shown to be statistically significant predictors of pre‐nasal /æ/ tensing. I argue that social network metrics operationalize important aspects of the sociolinguistic context and contribute to our understanding of factors influencing how Latinx speakers recruit locally significant sociolinguistic variables in linguistic performance. The data and analysis strongly argue against distinctiveness approaches to studies of language and ethnicity, where “racial categories are equated with empirically distinctive sets of linguistic features” (Rosa & Flores, 2017), by demonstrating that Latinx speakers participate in a local change‐in‐progress in ways that are shaped by the same types of sociolinguistic factors that shape linguistic variation generally. The analysis is based on excerpts from a series of interviews conducted with Latinxs in the city (n = 33) in 2017–2018. The interviews were transcribed and coded for tokens of /æ/. Participants were categorized into one of three systems of /æ/ realizations, and tokens of /æ/ were further analyzed using inferential statistics to determine which independent variables were significant predictors of pre‐nasal /æ/ tensing. This research contributes to a growing body of work rejecting distinctiveness approaches to the linguistic performance of minoritized speakers, focusing instead on the ways in which individual speakers recruit linguistic features in the negotiation of identity (Eckert, 2008, 2018; Rosa & Flores, 2017; King 2016, 2018) and helps advance our understanding of how linguistic ideologies and articulations of ethnicity shape linguistic performance.

Microgel dynamics within the 3D porous structure of transparent PEG hydrogels

We report an investigation on the effects of the confinement imposed by application-relevant poly(ethylene glycol) (PEG) hydrogel matrices with controlled porosity on the dynamics of soft microgels. Through a detailed characterization of the internal structure of the hydrogels at the nano and microscale, we were able to link the microgel dynamics, measured by particle tracking, to the 3D geometrical confinement imposed by the porous matrices. PEG hydrogels with a high degree of transparency and tunable pore sizes and volume fractions were obtained using freeze-thawing. We found that the porosity of the hydrogel networks is characterized by elongated channels having asymmetric sections, with the average size decreasing from about 7 to about 2 particle diameters, and the size distribution becoming narrower with increasing PEG content in the pre-reaction mixture. The microgel dynamics slowdown and change from diffusive to sub-diffusive as a result of the increasing confinement. The observed decrease in diffusivity is consistent with models of diffusion in cylindrical pores and can be attributed to hydrodynamic and steric effects in addition to geometrical constriction. A dependence of the effective diffusion coefficient on the pore volume fraction, which is unusually pronounced, suggests the presence of microgel-hydrogel interactions. Our results demonstrate that a detailed characterization of the 3D geometry of the porous network is of primary importance for the understanding of transport properties in complex, random porous media.

New insights into the Rhône–Simplon fault system (Swiss Alps) from a consistent earthquake catalogue covering 35 yr

SUMMARYSeismotectonic interpretations in regions characterized by low to moderate seismicity require consistent earthquake catalogues covering periods of several decades. Inevitable changes in network configuration and analysing procedures, however, introduce significant bias to the hypocentre parameters and uncertainty estimates reported in such catalogues. To overcome these limitations, we developed a procedure using coupled hypocentre-velocity inversions to compute consistent hypocentre locations covering time periods of several decades while accounting for changes in network geometry. We apply these procedures to 35 yr of instrumentally recorded seismicity along the Rhône–Simplon fault system in southwest Switzerland, which is at the transition between the Central and Western Alps. The entire catalogue is relocated using a probabilistic location algorithm in combination with the derived minimum 1-D velocity models. A combination of location parameters is used to define consistent location-quality classes allowing for reliable interpretation of epicentres and focal depths. The relocated catalogue is interpreted together with a recent 3-D P-wave tomographic model and available 2-D reflection seismic profiles. The relocated hypocentres indicate that the major band of seismicity north of the Rhône valley is associated with a 30–40 km long, steeply north-dipping shear zone, which roots in the crystalline basement of the Aar Massif and extends to the shallowest levels of the sedimentary cover of the Helvetic nappes in the Rawil Depression. Seismicity towards the southwest indicates the existence of a similar shear zone within the Aiguille Rouge Massif. This zone possibly extends to the northeast and joins the Rawil fault zone. To the south of the Rhône valley, seismicity is scattered within the Penninic nappes, but limited to the hanging wall of the Pennine Basal Thrust (PBT). The Penninic nappes are characterized by a relatively higher VP of about 5 per cent compared to the Aar Massif, indicating differences in composition or metamorphic grade across the PBT.

Measuring the superblock based on a hierarchy matrix of geometry, configuration, network, and area: The case of Nanjing

A superblock is a core unit of the built form of an old city in China, in which various morphological elements are organized and related through a hierarchical structure. Existing quantitative studies are generally limited to a single perspective or object and do not support the classification of morphological types through comprehensive analysis methods. In this study, a new cognitive framework, the hierarchy matrix, is presented to bridge this knowledge gap. It consists of four dimensions: configuration of network, geometry of network, configuration of area, and geometry of area. These dimensions are formed by the intersection of the two coordinates of perspective and object. Based on their measurement, the overall characteristics of the superblocks are represented and compared through matrix diagrams. Subsequently, the validity and adaptability of this quantitative approach are verified through an empirical analysis of Nanjing’s old city superblocks. The results reveal the morphological type of superblocks, and their causes are analyzed through the correlation with the urban environmental background. hierarchy matrix is potentially a useful method for studying the complex emerging built form of rapidly changing cities, especially in developing countries, such as China. The hierarchical matrix method is not only an analysis tool but also has the potential to develop an evaluation method to provide scientific support for the practice of urban renewal.

Introducing covariances of observations in the minimum L1-norm, is it needed?

Abstract The most common approaches for assigning weights to observations in minimum L1-norm (ML1) is to introduce weights of p or p \sqrt{p} , p being the weights vector of observations given by the inverse of variances. Hence, they do not take covariances into consideration, being appropriated only to independent observations. To work around this limitation, methods for decorrelation/unit-weight reduction of observations originally developed in the context of least squares (LS) have been applied for ML1, although this adaptation still requires further investigations. In this article, we presented a deeper investigation into the mentioned adaptation and proposed the new ML1 expressions that introduce weights for both independent and correlated observations; and compared their results with the usual approaches that ignore covariances. Experiments were performed in a leveling network geometry by means of Monte Carlo simulations considering three different scenarios: independent observations, observations with “weak” correlations, and observations with “strong” correlations. The main conclusions are: (1) in ML1 adjustment of independent observations, adaptation of LS techniques introduces weights proportional to p \sqrt{p} (but not p); (2) proposed formulations allowed covariances to influence parameters estimation, which is unfeasible with usual ML1 formulations; (3) introducing weighs of p provided the closest ML1 parameters estimation compared to that of LS in networks free of outliers; (4) weighs of p \sqrt{p} provided the highest successful rate in outlier identification with ML1. Conclusions (3) and (4) imply that introducing covariances in ML1 may adversely affect its performance in these two practical applications.

Programming the Self-Organization of Endothelial Cells into Perfusable Microvasculature.

The construction of three-dimensional (3D) microvascular networks with defined structures remains challenging. Emerging bioprinting strategies provide a means of patterning endothelial cells (ECs) into the geometry of 3D microvascular networks, but the microenvironmental cues necessary to promote their self-organization into cohesive and perfusable microvessels are not well known. To this end, we reconstituted microvessel formation in vitro by patterning thin lines of closely packed ECs fully embedded within a 3D extracellular matrix (ECM) and observed how different microenvironmental parameters influenced EC behaviors and their self-organization into microvessels. We found that the inclusion of fibrillar matrices, such as collagen I, into the ECM positively influenced cell condensation into extended geometries such as cords. We also identified the presence of a high-molecular-weight protein(s) in fetal bovine serum that negatively influenced EC condensation. This component destabilized cord structure by promoting cell protrusions and destabilizing cell-cell adhesions. Endothelial cords cultured in the presence of fibrillar collagen and in the absence of this protein activity were able to polarize, lumenize, incorporate mural cells, and support fluid flow. These optimized conditions allowed for the construction of branched and perfusable microvascular networks directly from patterned cells in as little as 3 days. These findings reveal important design principles for future microvascular engineering efforts based on bioprinting and micropatterning techniques. Impact statement Bioprinting is a potential strategy to achieve microvascularization in engineered tissues. However, the controlled self-organization of patterned endothelial cells into perfusable microvasculature remains challenging. We used DNA Programmed Assembly of Cells to create cell-dense, capillary-sized cords of endothelial cells with complete control over their structure. We optimized the matrix and media conditions to promote self-organization and maturation of these endothelial cords into stable and perfusable microvascular networks.

Deep Transfer Learning of Satellite Imagery for Land Use and Land Cover Classification

Deep learning has been instrumental in solving difficult problems by automatically learning, from sample data, the rules (algorithms) that map an input to its respective output. Purpose: Perform land use landcover (LULC) classification using the training data of satellite imagery for Moscow region and compare the accuracy attained from different models. Methods: The accuracy attained for LULC classification using deep learning algorithm and satellite imagery data is dependent on both the model and the training dataset used. We have used state-of-the-art deep learning models and transfer learning, together with dataset appropriate for the models. Different methods were applied to fine tuning the models with different parameters and preparing the right dataset for training, including using data augmentation. Results: Four models of deep learning from Residual Network (ResNet) and Visual Geometry Group (VGG) namely: ResNet50, ResNet152, VGG16 and VGG19 has been used with transfer learning. Further training of the models is performed with training data collected from Sentinel-2 for the Moscow region and it is found that ResNet50 has given the highest accuracy for LULC classification for this region. Practical relevance: We have developed code that train the 4 models and make classification of the input image patches into one of the 10 classes (Annual Crop, Forest, Herbaceous Vegetation, Highway, Industrial, Pasture, Permanent Crop, Residential, River, and Sea&Lake).

Weighted simplicial complexes and their representation power of higher-order network data and topology.

Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the adopted mathematical framework to describe higher-order networks starting from data of higher-order interactions. Unweighted simplicial complexes typically involve a loss of information of the data, though having the benefit to capture the higher-order topology of the data. In this work we show that weighted simplicial complexes allow one to circumvent all the limitations of unweighted simplicial complexes to represent higher-order interactions. In particular, weighted simplicial complexes can represent higher-order networks without loss of information, allowing one at the same time to capture the weighted topology of the data. The higher-order topology is probed by studying the spectral properties of suitably defined weighted Hodge Laplacians displaying a normalized spectrum. The higher-order spectrum of (weighted) normalized Hodge Laplacians is studied combining cohomology theory with information theory. In the proposed framework we quantify and compare the information content of higher-order spectra of different dimension using higher-order spectral entropies and spectral relative entropies. The proposed methodology is tested on real higher-order collaboration networks and on the weighted version of the simplicial complex model "Network Geometry with Flavor."

Factors Controlling the Flow and Connectivity in Fracture Networks in Naturally Fractured Geothermal Formations

Summary The productivity and injectivity of hydraulically fractured geothermal wells in naturally fractured formations depend on the connectivity of fracture networks created by the interaction of hydraulic fractures with natural fractures. The primary objectives of this paper are (a) to define quantitatively the connectivity of the created fracture network, (b) to determine the factors that control the connectivity of fracture networks bounded by wells, and (c) to propose ways in which the flow capacity and fracture connectivity can be improved by changes to the hydraulic fracture design. A fully 3D hydraulic fracturing simulator has been developed that considers the interaction of hydraulic fractures with natural fractures by solving for the stresses, fluid flow, heat transfer, fracture growth, and intersection. These propagated fractures, which include hydraulic fractures and reactivated natural fractures, are divided into backbone, dead-end, and isolated fractures. Different well patterns that aim to optimize the connectivity of the injector to the producer (optimize the area of the backbone fractures) are simulated. A sensitivity analysis is conducted to investigate the effect of various parameters on the connectivity of wells through fractures. An optimal well pattern is needed to maximize the connected fracture area that provides a conductive path for heat extraction from naturally fractured geothermal reservoirs. Our results show that the connectivity of fracture networks is dramatically impacted by the degree of deflection, crossing, and merging of hydraulic fractures with natural fractures. An example is used to investigate the effect of backbone and dead-end fractures on heat extraction from an enhanced geothermal system (EGS). The detailed parametric study helps us better understand the factors that influence the geometry and connectivity of fracture networks and guide us in hydraulic fracture design and well spacing optimization in naturally fractured geothermal reservoirs.

Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions

We derive the Hessian geometric structure of nonequilibrium chemical reaction networks on the flux and force spaces induced by the Legendre duality of convex dissipation functions and characterize their dynamics as a generalized flow. With this geometric structure, we can extend theories of nonequilibrium systems with quadratic dissipation functions to more general cases with nonquadratic ones, which are pivotal for studying chemical reaction networks. By applying generalized notions of orthogonality in Hessian geometry to chemical reaction networks, two generalized decompositions of the entropy production rate are obtained, each of which captures gradient-flow and minimum-dissipation aspects in nonequilibrium dynamics.

Experimental modelling of primary migration in a layered, brittle analogue system

A 2D Hele-Shaw cell was built to study microfracture nucleation, growth, and network formation during internal fluid production. Fluid is slowly produced into a low permeability solid, which leads to a local fluid pressure increase that controls the nucleation of microfractures that grow and then connect to create flow pathways. This process occurs during the primary migration of hydrocarbons in source rocks, which is the main topic of our study. It may also occur in other geological systems, such as the expulsion of water during dehydration of clay-rich sediments in sedimentary basins or serpentinite rocks in subduction zones and the transport of magmatic melts. Our system consists of a transparent, brittle gelatin material mixed with yeast and sugar. The consumption of sugar by yeast leads to CO2 formation, resulting in microfracture nucleation and growth. We varied three parameters, (1) anisotropy (i.e., number of layers), (2) lateral sealing, and (3) rate of fluid production. We tracked fluid movement through the opening and closing of microfractures within the system. Microfracture nucleation density is similar in a layered system to previous studies (0.45 microfracture per cm2). However, we observed that lateral confinement (0.31 microfracture per cm2) and rate of expulsion (0.99 microfracture per cm2) affect nucleation density and the geometrical characteristics of the microfracture network. The size, extent, and geometry of the microfracture network are dependent on all three parameters investigated, where lateral confinement and a higher rate of expulsion result in greater microfracture network connectivity. Layers control the angle of intersection between microfractures. Furthermore, layering and sealing have an impact on fracture topology. Results also show that the microfracture pattern significantly influences the fluid expulsion rate. Our results have direct applications to understanding how fluid migration occurs in low-permeability rocks through the development of a connected microfracture network produced by internal fluid generation.