Random Network Research Articles

Directed graphs with lower orientation Ramsey thresholds

We investigate the threshold p⃗H = p⃗H (n) for the Ramsey-type property G(n, p) → ⃗H, where G(n, p) is the binomial random graph and G → ⃗H indicates that every orientation of the graph G contains the oriented graph ⃗ H as a subdigraph. Similarly to the classical Ramsey setting, the upper bound p⃗H ⩽ Cn−1/m2(⃗ H) is known to hold for some constant C = C( ⃗ H), where m2(⃗H) denotes the maximum 2-density of the underlying graph H of ⃗ H. While this upper bound is indeed the threshold for some ⃗H, this is not always the case. We obtain examples arising from rooted products of orientations of sparse graphs (such as forests, cycles and, more generally, subcubic {K3, K3,3}-free graphs) and arbitrarily rooted transitive triangles.

Same old story with a different ending: Homophily and preferential selection of information within the US climate policy network.

The passage of the Inflation Reduction Act has been perceived as a substantial shift away from the history of more contentious climate politics in the US. We apply social network methods to interrogate an updated dataset that assesses the degree to which recent policy outcomes are a shift away from earlier policies and positions. We empirically test for homophily, a building block of polarisation, analysing four waves of survey data collected over 12 years from the community of political elites engaged in the issue of climate politics. Using Exponential Random Graph (ERG) modeling, we provide clear evidence that the stances of the top policy actors working on climate change have not shifted substantially. Instead, we document how the policy was successful due to its ability to combine the Administration's desire to support clean energy along with fossil fuel interests' aims of expanding extraction and profiting from a transition away from fossil fuels.

Spatial Structure of the Radio‐Frequency Noise Field in a Large City

AbstractThe urban radio‐frequency (RF) noise generated by our cities continues to change with time. Although models exist to describe the RF noise as functions of frequency and urban land use types, very few models describe the spatial character or structure of the noise on the scales of city blocks (50–150 m). The goal of this work is to investigate the connection between urban morphology and the higher‐order spatial statistics of the noise field. To achieve this goal, a large measurement campaign was conducted in Boston, Massachusetts. Many spatial measurements allowed for calculation of spatial correlation functions of noise power in three different neighborhoods, which were used to quantify the spatial structure of the fields. A statistical point source model is then developed, with adjustable parameters relating to urban morphology. Good agreement between the model and the experimental correlation functions suggests the 25 MHz urban noise field is well described by a random network of fixed point sources, radiating with a 1/r power law behavior.

Robust Point Cloud Registration via Random Network Co-Ensemble

Robust Point Cloud Registration via Random Network Co-Ensemble

Control of ecological networks: Abundance control or ecological regulation?

Complex ecosystems often exhibit a tipping point around which a small perturbation can lead to the loss of the basic functionality of ecosystems. It is challenging to develop a control strategy to bring ecosystems to the desired stable states. Typically, two methods are employed to restore the functionality of ecosystems: abundance control and ecological regulation. Abundance control involves directly managing species abundance through methods such as trapping, shooting, or poisoning. On the other hand, ecological regulation is a strategy for ecosystems to self-regulate through environment improvement. To enhance the effectiveness of ecosystem recovery, we propose adaptive regulation by combining the two control strategies from mathematical and network science perspectives. Criteria for controlling ecosystems to reach equilibrium with or without noise perturbation are established. The time and energy costs of restoring an ecosystem to equilibrium often determine the choice of control strategy, thus, we estimate the control costs. Furthermore, we observe that the regulation parameter in adaptive regulation affects both time and energy costs, with a trade-off existing between them. By optimizing the regulation parameter based on a performance index with fixed weights for time and energy costs, we can minimize the total cost. Moreover, we discuss the impact of the complexity of ecological networks on control costs, where the more complex the networks, the higher the costs. We provide corresponding theoretical analyses for random networks, predator-prey networks, and mixture networks.

Graph Embedded Ensemble Deep Randomized Network for Diagnosis of Alzheimer's Disease.

Randomized shallow/deep neural networks with closed form solution avoid the shortcomings that exist in the back propagation (BP) based trained neural networks. Ensemble deep random vector functional link (edRVFL) network utilize the strength of two growing fields, i.e., deep learning and ensemble learning. However, edRVFL model doesn't consider the geometrical relationship of the data while calculating the final output parameters corresponding to each layer considered as base model. In the literature, graph embedded frameworks have been successfully used to describe the geometrical relationship within data. In this paper, we propose an extended graph embedded RVFL (EGERVFL) model that, unlike standard RVFL, employs both intrinsic and penalty subspace learning (SL) criteria under the graph embedded framework in its optimization process to calculate the model's output parameters. The proposed shallow EGERVFL model has only single hidden layer and hence, has less representation learning. Therefore, we further develop an ensemble deep EGERVFL (edEGERVFL) model that can be considered a variant of edRVFL model. Unlike edRVFL, the proposed edEGERVFL model solves graph embedded based optimization problem in each layer and hence, has better generalization performance than edRVFL model. We evaluated the proposed approaches for the diagnosis of Alzheimer's disease and furthermore on UCI datasets. The experimental results demonstrate that the proposed models perform better than baseline models. The source code of the proposed models is available at https://github.com/mtanveer1/.

Structure-Mechanics Principles and Mechanobiology of Fibrocartilage Pericellular Matrix: A Pivotal Role of Type V Collagen.

The pericellular matrix (PCM) is the immediate microniche surrounding resident cells in various tissue types, regulating matrix turnover, cell-matrix cross-talk and disease initiation. This study elucidated the structure-mechanical properties and mechanobiological functions of the PCM in fibrocartilage, a family of connective tissues that sustain complex tensile and compressive loads in vivo. Studying the murine meniscus as the model tissue, we showed that fibrocartilage PCM contains thinner, random collagen fibrillar networks that entrap proteoglycans, a structure distinct from the densely packed, highly aligned collagen fibers in the bulk extracellular matrix (ECM). In comparison to the ECM, the PCM has a lower modulus and greater isotropy, but similar relative viscoelastic properties. In Col5a1 +/- menisci, the reduction of collagen V, a minor collagen localized in the PCM, resulted in aberrant fibril thickening with increased heterogeneity. Consequently, the PCM exhibited a reduced modulus, loss of isotropy and faster viscoelastic relaxation. This disrupted PCM contributes to perturbed mechanotransduction of resident meniscal cells, as illustrated by reduced intracellular calcium signaling, as well as upregulated biosynthesis of lysyl oxidase and tenascin C. When cultured in vitro, Col5a1 +/- meniscal cells synthesized a weakened nascent PCM, which had inferior properties towards protecting resident cells against applied tensile stretch. These findings underscore the PCM as a distinctive microstructure that governs fibrocartilage mechanobiology, and highlight the pivotal role of collagen V in PCM function. Targeting the PCM or its molecular constituents holds promise for enhancing not only meniscus regeneration and osteoarthritis intervention, but also addressing diseases across various fibrocartilaginous tissues.

A new relaying approach for protecting TCSC compensated transmission line connected to DFIG based wind farm

In modern power systems, Thyristor Controlled Series Capacitor (TCSC)-compensated transmission lines are crucial in transporting bulk power from large wind farms. However, the performance of conventional distance relays is adversely impacted by the typical fault characteristics of the Doubly Fed Induction Generator (DFIG) and TCSC. To address this challenge, this paper presents a new relaying algorithm such as Complete Ensemble Empirical Mode Decomposition with Adaptive Noise-based Dominant Mode Algorithm-Hilbert Transform (CEEMDAN-DMA-HT) for fault detection and CEEMDAN assisted Enhanced Jaya Optimization-based Random Vector Functional Link Network (EJAYA-RVFL) for fault classification. In proposed fault detection algorithm, the differential current from both ends of the line is subjected to Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, leading to the extraction of distinct intrinsic mode functions (IMFs). Employing the Dominant Mode Algorithm, the IMF with the highest Pearson correlation coefficient, referred to as the dominant IMF, is identified. Subsequently, a comparison between this dominant mode IMF and the original input signal is conducted after passing the obtained signal through the Hilbert Transform (HT), enabling effective fault detection. The proposed classifier leverages a straightforward feature set that quantifies the energy of each phase and the ground. These features serve as inputs for the proposed classifier, facilitating the categorization of different fault types. To evaluate the effectiveness of the proposed relaying algorithm, several fault and non-fault scenarios are simulated on a test power system using MATLAB/Simulink. The results demonstrate that; the proposed fault detection and classification algorithm are able to detect and classify faults in less than a half-cycle. The proposed method gives 100% fault accuracy for fault detection and 99.97 % accuracy for fault classification. Furthermore, the proposed classifier achieves the performance metrics like Precision (0.998), Recall (0.997) and F1-Score (0.996), providing quantitative insights into its accuracy and dependability. Finally, a comparative analysis is carried out with existing approaches.

Infiltration and permeability of porous ceramics simulated by random networks

A network computational model for a 3D ceramic structure is developed. The model is applied to study the impact of geometric and material parameters of structure on the liquid metal flow through random porous ceramic medium in pressure infiltration processes. The characteristic geometric features of the ceramic structure favorable for liquid metal flow during the infiltration process are determined. The method of structural approximation and constructive homogenization are applied, and the discrete stationary Stokes equations on random graphs are considered. This approach gives a robust algorithm to determine the macroscopic permeability K of interpenetrating phases. The dependencies of K on the distribution of connections (windows) between the cells (inclusions) are derived. The numerical simulations demonstrate that the permeability K does not depend on the scaled distribution sizes of windows. This implies that K is proportional to the mean value of the window areas. The considered model takes into account a random complex structure of 3D ceramic. Hence, it complements the previous study on the local transport properties of tubes (windows) connecting the cells.

Rényi mutual information in quantum field theory, tensor networks, and gravity

We explore a large class of correlation measures called the α − z Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the α − z RMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of α and z, the α − z RMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute the α − z RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.

Two‐sample testing for random graphs

Two‐sample testing for random graphs

Resilient leaderless and leader–follower consensus over random networks through [formula omitted]-hop communication

This paper studies the resilient consensus problems under ℓ-hop communication over directed random networks. We develop novel multi-hop protocols to tackle both leaderless and leader–follower consensus with a single leader when the multiagent system is under both attack from Byzantine agents and failure of communication edges. Our unified framework features a multiple-input multiple-output system design, and generalizes the weighted mean subsequence reduced algorithms, in which extremal values in the ℓ-hop neighborhood of a cooperative agent are censored based on the notion of minimum message cover. We establish conditions on dynamical network structures, under which secure consensus with vector states can be achieved in the sense of almost sure convergence.

Review of weighted exponential random graph models frameworks applied to neuroimaging.

Neuro-imaging data can often be represented as statistical networks, especially for functional magnetic resonance imaging (fMRI) data, where brain regions are defined as nodes and the functional interactions between those regions are taken as edges. Such networks are commonly divided into classes depending on the type of edges, namely binary or weighted. A binary network means edges can either be present or absent. Whereas the edges of a weighted network are associated with weight values, and fMRI networks belong to weighted networks. Statistical methods are often adopted to analyse such networks, among which, the exponential random graph model (ERGM) is an important network analysis approach. Typically ERGMs are applied to binary networks, and weighted networks often need to be binarised by arbitrarily selecting a threshold value to define the presence of the edges, which can lead to non-robustness and loss of valuable edge weight information representing the strength of fMRI interaction in fMRI networks. While it is therefore important to gain deeper insight in adopting ERGM on weighted networks, there only exists a few different ERGM frameworks for weighted networks; some of these are not directly implementable on fMRI networks based on their original proposal. We systematically review, implement, analyse and compare five such frameworks via a simulation study and provide guidelines on each modelling framework as well as conclude the suitability of them on fMRI networks based on a range of criteria. We concluded that Multi-Layered ERGM is currently the most suitable framework.

A visit generation process for human mobility random graphs with location-specific latent-variables: From land use to travel demand

This research introduces a novel mathematical framework for understanding collective human mobility patterns, integrating mathematical modeling and data analysis. It focuses on latent-variable networks to investigate the dynamics of human mobility using stochastic models. By analyzing origin–destination data, the study uncovers scaling relations and explores the economic implications of mobility patterns, particularly regarding the income elasticity of travel demand. The mathematical analysis begins with the development of a stochastic model based on inhomogeneous random graphs, constructing a visitation model with multipurpose drivers for travel demand. Through this model, the study gains insights into the structural properties and dynamic correlations of human mobility networks, deriving analytical solutions for key network metrics: visit distribution, assortativity behavior and clustering coefficient. Empirically, the study validates the model’s assumptions and reveals scaling behaviors in origin–destination flows within a region, reproducing statistical regularities observed in real-world cases. Notably, the model’s application to estimating income elasticity of travel demand provides significant implications for urban and transport economics. Overall, this research contributes to a deeper understanding of the interplay between human mobility and regional demographics and economics. It sheds light on critical scaling relations across various aspects of collective human mobility and underscores the importance of incorporating latent-variable structures into mobility modeling for accurate economic analysis and decision-making in urban and transportation planning.

The Evolution of Cooperation in a Mobile Population on Random Networks: Network Topology Matters Only for Low-Degree Networks

The Evolution of Cooperation in a Mobile Population on Random Networks: Network Topology Matters Only for Low-Degree Networks

One-way ticket to the moon? An NLP-based insight on the phenomenon of small-scale neo-broker trading

We present an Natural Language Processing based analysis on the phenomenon of “Meme Stocks”, which has emerged as a result of the proliferation of neo-brokers like Robinhood and the massive increase in the number of small-scale stock investors. Such investors often use specific Social Media channels to share short-term investment decisions and strategies, resulting in partial collusion and planning of investment decisions. The impact of online communities on the stock prices of affected companies has been considerable in the short term. This paper has two objectives. Firstly, we chronologically model the discourse on the most prominent platforms. Secondly, we examine the potential for using collaboratively made investment decisions as a means to assist in the selection of potential investments.. To understand the investment decision-making processes of small-scale investors, we analyze data from Social Media platforms like Reddit, Stocktwits and Seeking Alpha. Our methodology combines Sentiment Analysis and Topic Modelling. Sentiment Analysis is conducted using VADER and a fine-tuned BERT model. For Topic Modelling, we utilize LDA, NMF and the state-of-the-art BERTopic. We identify the topics and shapes of discussions over time and evaluate the potential for leveraging information of the decision-making process of investors for trading choices. We utilize Random Forest and Neural Network Models to show that latent information in discussions can be exploited for trend prediction of stocks affected by Social Network driven herd behavior. Our findings provide valuable insights into content and sentiment of discussions and are a vehicle to improve efficient trading decisions for stocks affected from short-term herd behavior.

Exponential synchronization of dynamical complex networks via random impulsive scheme

This paper investigates the synchronization of a complex network based on a class of random impulsive differential equation systems. Based on the random impulsive strategy of Poisson distribution, a random impulsive dynamical network model is constructed. Using the Lyapunov principle, random process theory, linear matrix inequality method, and some basic analysis methods, we realize the global mean-square index synchronization of the model. We then get sufficient criteria for the synchronization. By presenting a numerical example, we verified the validity of the theoretical results.

The Ordered Median Tree Location Problem

In this paper, we propose the Ordered Median Tree Location Problem (OMT). The OMT is a single-allocation facility location problem where p facilities must be placed on a network connected by a non-directed tree. The objective is to minimize the sum of the ordered weighted averaged allocation costs plus the sum of the costs of connecting the facilities in the tree. We present different MILP formulations for the OMT based on properties of the minimum spanning tree problem and the ordered median optimization. Given that ordered median location problems are rather difficult to solve we have improved the OMT solution performance by introducing covering variables in a valid reformulation plus developing two pre-processing phases to reduce the size of this formulations. In addition, we propose a Benders decomposition algorithm to approach the OMT. We establish an empirical comparison between these new formulations and we also provide enhancements that together with a proper formulation allow to solve medium size instances on general random graphs.

Spatio-temporal evolution and driving mechanism of metal value flow networks: A global value chain perspective

The lengthening of the global value chain (GVC) and the deepening of the transnational labor division system have led to frequent cross-border flows of metal values worldwide, and the pattern of the international metal trade is facing reconstruction. This paper combines a new trade accounting framework and a complex network model to construct global metal domestic value added (DVA) and foreign value added (FVA) flow networks based on global multi-regional input‒output (MRIO) tables for 2000 and 2007–2022 and then analyzes their structural topological features and spatio-temporal evolution trends at the macro, medium, and micro levels. Then, the main driving factors are investigated using the exponential random graph model (ERGM). The results show that the DVA and FVA networks are expanding and have obvious aggregation effects and small-world characteristics, that the community divisions show a trend toward regional integration and worldwide multipolarity, and that Germany is the most important transportation hub and trade medium in the FVA network, while China and the United States are, respectively, the largest creator and consumer of the world's metal value flow. In addition, the DVA network is more susceptible to node attribute effects such as GDP, trade openness, population size and foreign direct investment, while the FVA network is more susceptible to exogenous network effects such as geographic distance and colonial ties.

Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs

Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs