Graph Of Function Research Articles

Graph neural networks for predicting structural stability of Cd- and Zn-doped [formula omitted]-CsPbI3

Computational modeling of disordered crystal structures is essential for the study of composition–structure–property relations for many families of functional materials. Efficient and reliable solutions are of great interest due to the promising reduction of labor-intensive calculations through data-driven prediction of target properties. One of the modern problems directly related to this topic is the enhancement of phase stability of functional materials with the required properties. In this work, we address the effects of Cd and Zn substitutions on the Pb sites on the structural stability of inorganic lead halide perovskite CsPbI3 — a semiconductor promising for optoelectronic devices. At room temperature, this material undergoes an undesirable phase transition from the direct band gap “black” to indirect “yellow” (ca. 15 meV/atom more favored) phase. For evaluations of effects caused by the substitutions, we combined the density functional theory (DFT) calculations and graph neural network (GNN) models. At low Cd and Zn contents, complete composition/configuration spaces comprising ca. 200 structures were set and studied using DFT. The GNN models trained on this data were used to predict energetics of ca. 74k structures with higher contents of substitutions and evaluate the energy differences between the phases. Because of the small amount of DFT data, an impact of data subsampling on the quality of predictions was comprehensively studied. Additionally, transfer learning routines were tested using available collections of DFT-derived properties. For the examined models, the root-mean-square errors of ca. 0.7 meV/atom were achieved in predicting formation energies. The data treatment workflows proposed and tested in this study open up perspectives for data-driven research of disordered materials of particular interest with low computational costs.

Functional graph contrastive learning of hyperscanning EEG reveals emotional contagion evoked by stereotype-based stressors

IntroductionThis study delves into the intricacies of emotional contagion and its impact on performance within dyadic interactions. Specifically, it focuses on the context of stereotype-based stress (SBS) during collaborative problem-solving tasks among female pairs. Through an exploration of emotional contagion, this study seeks to unveil its underlying mechanisms and effects.MethodsLeveraging EEG-based hyperscanning technology, we introduced an innovative approach known as the functional graph contrastive learning (fGCL), which extracts subject-invariant representations of neural activity patterns from feedback trials. These representations are further subjected to analysis using the dynamic graph classification (DGC) model, aimed at dissecting the process of emotional contagion along three independent temporal stages.ResultsThe results underscore the substantial role of emotional contagion in shaping the trajectories of participants' performance during collaborative tasks in the presence of SBS conditions.DiscussionOverall, our research contributes invaluable insights into the neural underpinnings of emotional contagion, thereby enriching our comprehension of the complexities underlying social interactions and emotional dynamics.

Zygmund graphs are thin for doubling measures

The Zygmund functions form an intermediate class between Lipschitz and Hölder functions; their second order divided differences are uniformly bounded. It is well known that for d≥1 the graph of any Lipschitz function f:Rd→R is thin for doubling measures, and we extend this result to the Zygmund class.

Rough Set Techniques in Wireless Sensor Networks using Membership Function and Rough Labelling Graphs for Energy Aware Routing

Rough set theory and rough graphs are employed for data analysis. Rough graphs utilize approximations, and this paper presents a method for implementing rough graphs using rough membership functions and graph labeling for data structures and reduction. This paper proposes a rough graph labeling method, termed rough -labeling similarity graph, that utilizes a similarity measure for vertex and edge labeling. This method aims to minimize boundary regions in rough graphs and is applicable to wireless sensor networks (WSNs). In WSN, the proposed algorithms such as PSO-LSTM, COA-LSTM, LOA-LSTM integrates with rough set theory based rough -labeling for boundary region identification. The proposed method incorporates the membership functions encapsulates the rough labeling graphs for cluster boundary region identification for WSN. The cluster boundary for WSN is based on rough set membership and rough labelling is termed as rough set membership boundary region (RMB). RMB in WSN and implementation of proposed routing algorithm such as LOA-LSTM provides high throughput and energy saving when compared to existing cluster boundary structure methods such as Voronoi, Spectrum and Chain.

Two-layer neural network on infinite-dimensional data: global optimization guarantee in the mean-field regime *

The analysis of neural network optimization in the mean-field regime is important as the setting allows for feature learning. The existing theory has been developed mainly for neural networks in finite dimensions, i.e. each neuron has a finite-dimensional parameter. However, the setting of infinite-dimensional input naturally arises in machine learning problems such as nonparametric functional data analysis and graph classification. In this paper, we develop a new mean-field analysis of a two-layer neural network in an infinite-dimensional parameter space. We first give a generalization error bound, which shows that the regularized empirical risk minimizer properly generalizes when the data size is sufficiently large, despite the neurons being infinite-dimensional. Next, we present two gradient-based optimization algorithms for infinite-dimensional mean-field networks, by extending the recently developed particle optimization framework to the infinite-dimensional setting. We show that the proposed algorithms converge to the (regularized) global optimal solution, and moreover, their rates of convergence are of polynomial order in the online setting and exponential order in the finite sample setting, respectively. To the best of our knowledge, this is the first quantitative global optimization guarantee of a neural network on infinite-dimensional input and in the presence of feature learning.

Joint VNF Parallelization and Deployment in Mobile Edge Networks

Mobile edge computing (MEC) has emerged as a promising computing paradigm that provides flexible and responsive local services for mobile user equipment at the network edge. Software instances for user equipment tasks are typically deployed as Virtualized Network Functions (VNFs) at resource-constrained edge nodes. Task data exchanged across the VNFs in serial can incur high task completion latency. It is therefore desirable to deploy certain VNFs in parallel. However, deciding where to deploy VNFs depends on which VNFs are parallel, and conversely, their deployment also affects their parallel execution. In this paper, for the first time, we jointly consider the parallelization and deployment strategies for VNFs at edge nodes. We closely examine the complexity of the joint optimization problem and introduce an Improved Service Function Graph (I-SFG) that reflects the coordination and dependency relations among the VNFs to provide parallel services for each piece of user equipment. We first propose an approach based on integer linear programming to find optimal solutions in small-scale scenarios and then present an effective solution through cascading I-SFG construction and VNF deployment approximation to solve large-scale problems. Theoretical analyses and experimental results show the superiority of our joint design and the proposed practical solution.

Properties of Graph Based on Divisor-Euler Functions

Divisor function gives the residues of which divide it. A function denoted by counts the total possible divisors of and gives the list of co-prime integers to . Many graphs had been constructed over these arithmetic functions. Using and , a well known graph named as divisor Euler function graph has been constructed. In this paper, we use divisor function and anti Euler function . We label the symbol to count those residues of which are not co-prime to . By using these functions, we find a new graph, called divisor anti-Euler function graph (DAEFG), denoted as . Let be a DAEFG, where and . The objective of this sequel is to introduce and discuss the properties of DAEFG. In this work, we discuss novel classes of proposed graph with its structure using loops, cycles, components of graph, degree of its vertices, components as complete, bipartite, planar, Hamiltonian and Eulerian graphs. Also, we find chromatic number, chromatic index and clique of these graphs.

Exploring the path of environmental visual design based on the perspective of new media

Abstract This paper first constructs a convolutional neural network model by convolutional layer, activation layer and normalization layer and then uses the style migration algorithm and image semantic segmentation algorithm based on the convolutional neural network to construct an environmental visual design model based on the style migration algorithm. The experimental analysis of the effective application of the environmental visual design scheme under the new media perspective is conducted after data pre-processing. The results show that from the total loss function graph after weighting, the function decreases from 0.03 to 0.01 after a small fluctuation, and the style migration imaging tends to a stable state, and the model is optimal now. This demonstrates the exploration of environmental visual design and encourages the innovative development of visual design in the new media environment.

Graphical solutions to one-phase free boundary problems

Abstract We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient dimensions, a one-phase free boundary analogue of Bernstein’s problem for minimal surfaces. As an application, we also classify monotone solutions of semilinear equations with a bump-type nonlinearity.

Development of an experimental prototype of a manufacturing cell for process automation teaching

For the industrial sector, the filling, sealing and labeling system represents one of the most used processes with several applications, that involves the food and beverage industry until the chemical plants, among many others applications. The propouse of this work is to develop an academic prototype of a manufacturing cell for teaching the automation of industrial processes, in order to emulate the filling, sealing and labeling system. The goal is to design a learning methodology such that the acquired academic knowledge can be transported to a real industrial environment. To achieve this, the PLC S7-300, industrial proximity sensors, pneumatic cylinders of the Festo brand, as well as their respective solenoid valves, are used. The programming methodology is based on a functional graph controlled by stages and transitions (GRAFCET). In contrart with other project based on Arduino, this project employs standard signals and variable scaling.

A Graph-Based Technique for Securing the Distributed Cyber-Physical System Infrastructure

Spreading digitalization, flexibility, and autonomy of technological processes in cyber-physical systems entails high security risks corresponding to negative consequences of the destructive actions of adversaries. The paper proposes a comprehensive technique that represents a distributed functional cyber-physical system’s infrastructure as graphs: a functional dependencies graph and a potential attacks graph. Graph-based representation allows us to provide dynamic detection of the multiple compromised nodes in the functional infrastructure and adapt it to rolling intrusions. The experimental modeling with the proposed technique has demonstrated its effectiveness in the use cases of advanced persistent threats and ransomware.

Simulation Cognitive Modeling Approach to the Regional Sustainable Complex System Development for Improving Quality of Life

This article presents study results of the region’s sustainable development possibility, thus improving the population’s life quality using cognitive simulation methods of complex systems. The main theoretical provisions of cognitive modeling developed and tested earlier in various socioeconomic system modeling are briefly outlined. The cognitive modeling application’s mathematical apparatus and CMCS software No. 2018661506 system were developed using quantitative data from one of Russia’s southern regions (Rostov oblast). The task was to study the region, model, understand, explain, and develop possible situation development scenarios, and foresee this complex system’s possible future outcome. The main statistical socioeconomic indicators of the state region were studied and processed. Data analysis necessary for developing and researching a cognitive model is given. The regional economic mechanism cognitive model is a functional graph consisting of quantitative and qualitative concepts. Between them, relationships are given in the form of functions, which is the novelty of research. The results of several scenarios of impulse modeling are presented, making it possible to predict future desirable and undesirable processes in the system. Scenario analysis was carried out, making it possible to propose a number of recommendations for the region’s sustainable development. A direction for the region’s development of further cognitive research is proposed.

Model discovery of compartmental models with Graph-Supported Neural Networks

In this proposal, our objective is to create a neural network for the discovery of models using compartmental models as systems of Ordinary Differential Equations (ODEs), employing Graph-Supported Neural Networks (GSNN). We design the GSNN as a graph of transition functions of the structure of the model to ensure that the three properties of the ODE solution are satisfied: additivity to one, positivity, and boundness. Rather than directly estimating the solution, these neural networks approximate the transition functions. We present theoretical evidence substantiating that our GSNN maintains these properties, along with approximation outcomes from both simulated and real-world data. These outcomes demonstrate that our GSNN outperforms the non-graph-supported approach for these issues, with instances where it even surpasses full model-based solutions and Recurrent Neural Networks. Furthermore, an evolutionary algorithm successfully generated a consistent model using the data, offering a comprehensive framework for neural network-based model discovery in these scenarios.

Transmuted Modified Weibull Distribution for Modeling Skewed Lifetime Dataset; Properties and Application

A new five parameter model called Generalized Modified Weibull distribution is proposed and studied. The new distribution generalizes the Modified Weibull Distribution introduced by Lai et al. (2003) using transformed – Transformer framework of Alzaatreh et al. (2014) which resulted to a distribution capable of modeling skewed data (positively or negatively skewed data), as well as, symmetric data. Property of a proper probability density function was used to ascertain that the resulting function is a proper probability density function. Statistical properties of the newly generated distribution were studied. Graph of probability density function of the distribution was used to show that it is capable of modeling skewed data. Graph of cumulative density functions of the distribution was plotted using varying parameter values. Monte Carlo simulation approach was used for the test of homogeneity of the distribution and it was observed that the parameters in the distribution approach the true values as sample size increases. Maximum likelihood Estimation method was used for estimation of the model parameters. Real life dataset was used for model comparison as well as demonstration of its application.

Multivariate Zipper Fractal Functions

A novel approach to zipper fractal interpolation theory for functions of several variables is presented. Multivariate zipper fractal functions are constructed and then perturbed through free choices of base functions, scaling functions, and a binary matrix called signature to obtain their zipper α-fractal versions. In particular, we propose a multivariate Bernstein zipper fractal function and study its coordinate-wise monotonicity which depends on the values of signature. We derive bounds for the graph of a multivariate zipper fractal function by imposing conditions on the scaling factors and the Hölder exponent of the associated germ function and base function. The box dimension result for multivariate Bernstein zipper fractal function is derived. Finally, we study some constrained approximation properties for multivariate zipper Bernstein fractal functions.

Multi-Connectivity Representation Learning Network for Major Depressive Disorder Diagnosis.

The pathophysiology of major depressive disorder (MDD) has been demonstrated to be highly associated with the dysfunctional integration of brain activity. Existing studies only fuse multi-connectivity information in a one-shot approach and ignore the temporal property of functional connectivity. A desired model should utilize the rich information in multiple connectivities to help improve the performance. In this study, we develop a multi-connectivity representation learning framework to integrate multi-connectivity topological representation from structural connectivity, functional connectivity and dynamic functional connectivities for automatic diagnosis of MDD. Briefly, structural graph, static functional graph and dynamic functional graphs are first computed from the diffusion magnetic resonance imaging (dMRI) and resting state functional magnetic resonance imaging (rsfMRI). Secondly, a novel Multi-Connectivity Representation Learning Network (MCRLN) approach is developed to integrate the multiple graphs with modules of structural-functional fusion and static-dynamic fusion. We innovatively design a Structural-Functional Fusion (SFF) module, which decouples graph convolution to capture modality-specific features and modality-shared features separately for an accurate brain region representation. To further integrate the static graphs and dynamic functional graphs, a novel Static-Dynamic Fusion (SDF) module is developed to pass the important connections from static graphs to dynamic graphs via attention values. Finally, the performance of the proposed approach is comprehensively examined with large cohorts of clinical data, which demonstrates its effectiveness in classifying MDD patients. The sound performance suggests the potential of the MCRLN approach for the clinical use in diagnosis. The code is available at https://github.com/LIST-KONG/MultiConnectivity-master.

Two-dimensional vector field of the phase energy spectrum application for motion identification

In the tasks of determining the location of objects and identifying movement, it is important to use the phase information contained in the phase-frequency spatial spectrum. In these problems, the phase-energy spectrum can be applied, which combines the advantages of the energy and phase spectra. A frame of a video sequence can be associated with a discrete vector field of the phase-energy spectrum; its components are located throughout the image. No less informative, but much simpler for analysis, is the discrete vector field of phase-energy characteristics. Its components are formed by the amplitudes of the harmonics of the phase-energy spectrum of a two-dimensional frame. To use the vector field of phase-energy characteristics in algorithms for identifying dynamic objects, information about interframe changes in its components is important. In this paper, the features of the change in the components of the vector field for the cases of horizontal and vertical movement of a rectangular object of constant brightness against a homogeneous background are investigated. Graphical representations of scalar fields of phase-energy functions are given. Characteristic regions are identified and their projections onto the coordinate plane are made. It is shown that two characteristic areas are the near and far hills, by analyzing which it is possible to determine the spatial coordinates of the object before the start of movement and the value of the object's inter-frame shift. The special areas of scalar fields of phase-energy functions are determined for the case of object motion in an arbitrary direction. It has been established that the presence of extended extrema in the graphs of phase-energy functions indicates a strictly vertical or horizontal movement of the object, and the presence of point extrema indicates the movement of the object “at an angle”, and the boundaries of the moving object and the magnitude of its displacement horizontally and vertically are completely determined by the coordinates of the point extrema. A number of options for finding the parameters of objects by extremums and/or by the boundaries of characteristic regions of phase-energy functions are proposed. The "boundary" and "extreme" approaches can be applied in vision systems as both an additional and a main tool for motion identification.

Results of capillary studies digital processing and interpretation with the aim of a pore channel size distribution function constructing

Pore channels distribution in reservoir by size largely determines such filtration parameters as absolute and phase permeability, as well as the residual oil saturation of the productive reservoir. This paper presents a technique for capillary research data digital processing in order to obtain a function graph of reservoir pore channels by size distribution. In this case, a generalized mathematical model of capillary pressure curves is used. The generalized model makes it possible to increase the accuracy of capillary curves approximation in the medium and small pore channels area. In this regard, the proposed digital processing technique makes it possible to increase the accuracy and efficiency of constructing the pore channel size distribution function. Keywords: pore channels; distribution density; permeability; oil saturation; digital processing technique.

Artificial paradises: Man-made sites for the conservation of amphibians in a changing climate

Mediterranean wetlands harbour a rich freshwater biodiversity but also rank among the most-climate and human-pressure sensitive habitats. Amphibians are a taxonomic group strongly dependent on wetlands and the most threatened class of vertebrates due to habitat loss and alteration. In the Mediterranean region, amphibians breed in a large variety of artificial water sites (AWS). We used a large dataset of amphibian breeding sites to model functional connectivity, graph theory and climate niche modelling. AWS are radically different in structure compared to natural ones (NWS). Thus, we have disclosed how AWS can serve as a key piece of the ecological connectivity for amphibian populations; AWS and NWS have comparable values at the landscape scale, but in some areas AWS are pivotal. Furthermore, many AWS contribute by buffering the effect of climate change in the near future. We emphasize that conservation management strategies would be strengthened by including a specific focus on human-made aquatic habitats.

Capturing cascading effects under urban flooding: A new framework in the lens of heterogeneity

Increasing urban flooding posed serious threat to urban safety and sustainable development. The heterogeneity of hazard-bearing bodies is one of the important reasons for the variability of cascading failure scenarios in floods. Most previous studies have focused on failure propagation risks among specific types of hazard-bearing bodies, making it impossible to conduct a systematic analysis of the damage caused by persistent flooding in cities. In contrast to conventional graph representations, the heterogeneous hazard-bearing bodies network (HHBBN) based on heterogeneous functional graph theory was constructed in this paper and used to capture the relevant associations of urban resources in a flood. The HHBBN takes into account heterogeneity such as sensitivity and service diffusivity, and functionalities related to hazard-bearing bodies are represented as nodes, with service relationships and geographical associations depicted as edges. To further study the performance change of HHBBN in urban areas during rainstorm flooding, the cascading failure of HHBBN under continuous disturbance was also simulated. The proposed network modeling and cascading failure simulation methods were tested in Futian District of Shenzhen City, China. The case results demonstrate that the heterogeneous hazard-bearing bodies are interdependent and networked, which causes flood damage to spread more quickly and widely. Furthermore, the larger degree and more propagating hazard-bearing bodies are the key factors affecting the cascading failure of heterogeneous hazard-bearing bodies.