Graph Of Function Research Articles

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.

The Development of Problem Based Learning Desmos-Assisted Digital Worksheet for Trigonometry Function

Research purposes was to develop digital Student Worksheets (LKPD) based on the Problem Based Learning (PBL) approach on trigonometry material using Desmos and to find out the feasibility analysis this worksheets. The research method uses Analysis Design Development Implementation Evaluation (ADDIE). In the analysis stage, literature studies, observations and interviews were carried out to find out difficulties during blended learning, followed by designing and developing media by utilizing the various features in Desmos. At the implementation stage, validation is carried out to test the feasibility of the e-LKPD by two experts on media and materials. The results of the expert validation on the feasibility of the e-LKPD on the media aspect obtained a value of 73,14% with the appropriate criteria, while the material aspect obtained a value of 75,00% with the appropriate criteria. The most prominent of this e-LKPD is animation which shows the interactiveness and able to spur students to discover and generalize the concept of the graph of the sine function of the unit circle. In the final stage a limited test was conducted in a small group of six students at SMAN 1 Lembang and get a response score of 76,74% was obtained with very good criteria.

Study on the ice friction characteristics

Ice friction plays a vital role in different fields, including glaciology, polar runways, and winter sports, the mechanisms of which are complex and affected by many parameters, such as temperature, velocity, and load. It is commonly accepted that the frictional characteristics of ice can be attributed to a lubricating layer. Sphere-on-ice friction experiments were conducted to study the influence of temperature, pressure, and velocity on ice friction. The lubrication state of ice friction under different conditions was analyzed, and it was found that the contact angle and roughness were crucial factors. Characterizations of the worn surfaces done using scanning electron microscopy (SEM), energy dispersive spectrometry (EDS) and three-dimensional white-light interference indicated that abrasive and oxidation wear were the main wear mechanisms arising from ice friction. The underlying mechanism was explored using molecular dynamics (MD) simulations. The results suggested that the effects of velocity, temperature, and load on the presence of hydrogen bonding alter the fluidity of the lubricating layer existing between the ice and sphere, which in turn affects the ice friction characteristics. In the lubricating layer, the concentrations of water molecules near the sliders and ice were higher than those in the inner water. Moreover, the adsorption energy verified that water molecules tended to be adsorbed on the ice and sliders. In addition, the calculation results indicated that some water molecules were re-oriented in the ice friction because spikes were observed in the radial distribution function (RDF) graphs.

Correction to: Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields

Correction to: Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields

Fractal hypersurfaces, affine Weyl groups, and wavelet sets

In this expository paper, we present some fundamental connections between iterated function systems, in particular those whose attractors are the graphs of multivariate real-valued fractal functions, and foldable figures, affine Weyl groups, and wavelet sets.

Smoothness analysis and approximation aspects of non-stationary bivariate fractal functions

The present note aims to establish the notion of non-stationary bivariate α-fractal functions and discusses some of their approximation properties. We see that using a sequence of iterated function systems generalizes the existing stationary fractal interpolation function (FIF). Also, we show the existence of Borel probability fractal measures supported on the graph of the non-stationary fractal function. Further, we define a fractal operator associated with the constructed non-stationary FIFs, and many applications of this operator such as fractal approximation and the existence of fractal Schauder bases are observed. In the end, we study the constrained approximation with the proposed interpolant.

Global and Local Connectivities Describe Hydrogen Intercalation in Metal Oxides.

We introduce global connectivity, Ω, which quantifies the detailed connectivity of a material and accurately captures reactivity behavior. We demonstrate that combining global and local connectivity describes how metal oxides interact with hydrogen. Blending density functional theory, graph theory, and machine learning we built a reactivity model which accurately predicts hydrogen intercalation potentials of different metal oxides experimentally measured in the lab. The use of global connectivity can accelerate materials design through the development of novel structure-property relationships.

Service Function Chaining and Embedding With Heterogeneous Faults Tolerance in Edge Networks

In the 5G-and-beyond era, ultra-reliable low latency communication (URLLC) services are ubiquitous in edge networks. To enhance the performance metrics and the quality of service (QoS), URLLC services are delivered via a sequence of software-based network functions, also known as a service function chain (SFC). Towards reliable SFC delivery, it is imperative to incorporate fault-tolerance during SFC deployments. However, deploying an SFC with fault-tolerance is challenging because the protection mechanism needs to jointly consider multiple concurrent physical/virtual network failures and hardware/software failures. Considering these concurrent heterogeneous failures, this work investigates how to effectively deliver an SFC in edge networks with the objective of minimizing bandwidth resource consumption. First, we introduce the concept of k-heterogeneous-faults-tolerance and propose an augmented protection graph, called k-connected service function slices layered graph (KC-SLG). Based on the KC-SLG, we formulate a novel problem called k-heterogeneous-faults-tolerant SFC embedding and propose an effective algorithm, called fault-tolerant service function graph embedding (FT-SFGE). FT-SFGE employs two proposed techniques: k-connected network slicing (KC-NS) and k-connected function slicing (KC-FS). Via thorough mathematical proofs, we show that KC-NS is 2-approximate. Extensive simulations show that KC-FS has the best average cost-efficiency when k = 2, and FT-SFGE outperforms the schemes directly extended from the state-of-the-art.

Modelling of thermal behaviour in niobium during electron beam welding

Niobium (Nb) has been the subject of extensive research for its application as a crucial material for various complex engineering systems. The increased usage of Nb has prompted extensive research into new ways to join it. Previous works done by researchers on niobium joining majorly involves the use of laser welding technology. In recent years, electron beam welding (EBW) has emerged as one of the most effective joining methods, with a poor understanding of the dynamics though. This study aimed to enhance our understanding of the EBW of Nb plates through the development of a novel finite-element multiphysics model and a molecular dynamics analysis. To understand the heat transmission during the welding process, this study developed heat distribution and temperature contour maps. Variations of several process parameters on heat distribution and beam stabilisation were also noted during the finite element analysis. This study also comprehends the physics behind the creation of keyhole geometry. Molecular dynamics analysis introduced Voronoi clusters and radial distribution function graphs to explain the successful macro- and atomistic evolution of the heat distribution during electron beam welding of pure niobium. The research in this literature discusses the experimentation correlated with computational and molecular dynamics modelling. The finite element modelling and the atomistic simulation provide the relation between heat dissipation through the liquid and solid phases of pure Nb and its behaviour at the molecular level. Niobium has a growing future potential in various engineering domains ranging from uses in spacecraft structures to heavy drilling machinery due to its astonishing thermal properties. These structures perform in extreme thermal conditions and thus addition of niobium in these systems can improve their integrity under such environment. EBW has proven to be a very efficient method for joining of materials and thus can be used for highly sophisticated equipment with marginal error. The studies can help provide useful insight in joining of Niobium and its alloys with near perfection which have been used extensively in recent times.

P℘N functions, complete mappings and quasigroup difference sets

AbstractWe investigate pairs of permutations of such that is a permutation for every . We show that, in that case, necessarily for some complete mapping of , and call the permutation a perfect nonlinear (PN) function. If , then is a PcN function, which have been considered in the literature, lately. With a binary operation on involving , we obtain a quasigroup, and show that the graph of a PN function is a difference set in the respective quasigroup. We further point to variants of symmetric designs obtained from such quasigroup difference sets. Finally, we analyze an equivalence (naturally defined via the automorphism group of the respective quasigroup) for PN functions, respectively, for the difference sets in the corresponding quasigroup.

V-Gas: Generating High Gas Consumption Inputs to Avoid Out-of-Gas Vulnerability

Out-of-gas errors occur when smart contract programs are provided with inputs that cause excessive gas consumption and which will be easily exploited to perform Denial-of-Service attacks. Various approaches have been proposed to estimate the gas limit of a function in smart contracts to avoid such error. However, underestimation often occurs when the contract is complex In this work, we propose V-Gas, which automatically generates inputs that maximize the gas cost and reduce underestimation. V-Gas is designed based on static analysis and feedback-directed mutational fuzz testing. First, V-Gas builds the gas weighted control flow graph of functions in smart contracts. Then, V-Gas develops gas consumption guided selection and mutation strategies to generate the input that maximize the gas consumption. For evaluation, we implement V-Gas based on js-evm, a widely used Ethereum virtual machine written in Javascript, and conduct experiments on 736 real-world transactions recorded on Ethereum. A total of 44.02% of the transactions would have out-of-gas errors based on the estimation results given by solc, meaning that the recorded real gas consumption for those transactions is larger than the gas limit estimated by solc. In comparison, V-Gas could reduce the underestimation ratio to 13.86%. To evaluate the performance of feedback-directed engine in V-Gas, we implemented other directed fuzzing engines and compared their performance with that of V-Gas. The results showed that V-Gas generates the same or higher gas estimation value on 97.8% of the transactions with less time, usually within 5 minutes. Furthermore, V-Gas has exposed 25 previously unknown out-of-gas vulnerabilities in widely used smart contracts, 6 of which have been assigned unique CVE identifiers in the U.S. National Vulnerability Database.

Variation in functional networks between clinical and subclinical discharges in childhood absence epilepsy: A multi-frequency MEG study

ObjectiveTwo types of spike-and-wave discharges (SWDs) exist in childhood absence epilepsy (CAE): clinical discharges are prolonged and manifest primarily as impaired consciousness, whereas subclinical discharges are brief with few objectively visible symptoms. This study aimed to compare neural functional network and default mode network (DMN) activity between clinical and subclinical discharges to better understand the underlying mechanism of CAE. MethodsUsing magnetoencephalography (MEG) data from 21 patients, we obtained 25 segments each of clinical discharges and subclinical discharges. Amplitude envelope correlation analysis was used to construct functional networks and graph theory was used to calculate network topological data. We then compared differences in functional connectivity within the DMN between clinical and subclinical discharges. All statistical comparisons were performed using paired-sample tests. ResultsCompared to subclinical discharges, the functional network of clinical discharges exhibited higher synchronization — particularly in the parahippocampal gyrus — as early as 10 s before the seizure. Additionally, the functional network of clinical SWDs presented an anterior shift of key nodes in the alpha frequency band. Regarding clinical discharge progression, there were gradual increases in the parameter node strengths (S), clustering coefficients (C), and global efficiency (E) of the functional networks, while the path lengths (L) decreased. These changes were most prominent at the onset of discharges and followed by some recovery in the high-frequency bands, but no significant change in the low-frequency bands. Furthermore, connections within the DMN during the discharge period were significantly stronger for clinical discharge compared to subclinical discharges. ConclusionsThese findings suggest that a more regular network before abnormal discharges in clinical discharges contributes to SWD explosion and that the parahippocampal gyrus plays an important role in maintaining oscillations. An absence seizure is a gradual process and the emergence of SWDs may be accompanied by initiation of inhibitory mechanisms. Enhanced functional connectivity among DMN brain regions may indicate that patients have entered a state of introspection, and functional abnormalities in the parahippocampal gyrus may be associated with patients' transient memory loss.

Distribution of number of observations required to obtain a cover for the support of a uniform distribution

For a given positive number ‘δ′, we consider a sequence of δ − neighborhoods of the independent and identically distributed (i.i.d.) random variables, from a U ( 0 , 1 ) distribution, and “stop as soon as their union contains the interval ( 0 , 1 ) . ” We call such a union “a cover.” To find the distributions of N ( δ ) , the stopping time random variable, we need the joint distribution of order statistics from a U ( 0 , 1 ) distribution. For each δ > 0 and n = 1 , 2 , … , we obtain a general expression for P ( N ( δ ) ≤ n ) , and for a fixed value of δ , it is the distribution function of N ( δ ) . For a given n, let Δ ( n ) be the minimum value of δ , so that the union of the n δ − neighborhoods of the first n observations contains the interval ( 0 , 1 ) . Because N ( δ ) ≤ n if and only if Δ ( n ) ≤ δ , the distributions of Δ ( n ) can be obtained by fixing n in the general expression for P ( N ( δ ) ≤ n ) . To describe the impact of δ on the distribution of N ( δ ) and that of n on Δ ( n ) , we sketch the graphs of distribution functions and the empirical distribution functions.

Cognitive modeling as a tool for selecting massive open online courses for independent work of students of general engineering areas of training in physics

Introduction. The article is devoted to the development of an adaptive mechanism for managing the independent work of students of general engineering areas when studying a physics course by using massive open online courses based on cognitive modeling technology. Purpose setting. The problem of choosing the factors that determine the feasibility of choosing massive open online courses for self-study of physics is being studied, and the sensitivity of the educational result to changes in influencing factors has been experimentally assessed. Methodology and methods of the study. The complex and weakly structured task of assessing the feasibility of using massive open online courses in teaching physics to students is formalized by constructing cognitive maps that allow modeling changes in the academic result with an impulsive change in factors and in the formation of scenarios. The research methodology is based on the qualitative principles of graph theory, PEST methodology and SWOT analysis. Results. A cognitive model is presented in the form of a functional graph and a simulation experiment was carried out to test the adequacy of the formed cognitive model. Conclusion. The results obtained should subsequently become the ground for the formation of a scientific basis for managing the quality of education in terms of selecting massive open online courses for independent work of students and increasing its both internal and external efficiency.