Graph Of Function Research Articles

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.

Intersecting families of graphs of functions over a finite field

Let U be a set of polynomials of degree at most k over Fq, the finite field of q elements. Assume that U is an intersecting family, that is, the graphs of any two of the polynomials in U share a common point. Adriaensen proved that the size of U is at most qk with equality if and only if U is the set of all polynomials of degree at most k passing through a common point. In this manuscript, using a different, polynomial approach, we prove a stability version of this result, that is, the same conclusion holds if |U| > qk − qk − 1. We prove a stronger result when k = 2. For our purposes, we also prove the following results. If the set of directions determined by the graph of f is contained in an additive subgroup of Fq, then the graph of f is a line. If the set of directions determined by at least q - sqrt{q}/2 affine points is contained in the set of squares/non-squares plus the common point of either the vertical or the horizontal lines, then up to an affinity the point set is contained in the graph of some polynomial of the form αxpk.

Real-Time Forecasting of Dockless Scooter-Sharing Demand: A Spatio-Temporal Multi-Graph Transformer Approach

Accurately forecasting the real-time travel demand for dockless scooter-sharing is crucial for the planning and operations of transportation systems. Deep learning models provide researchers with powerful tools to achieve this task, but research in this area is still lacking. This paper thus proposes a novel deep learning architecture named Spatio-Temporal Multi-Graph Transformer (STMGT) to forecast the real-time spatiotemporal dockless scooter-sharing demand. The proposed model uses a graph convolutional network (GCN) based on adjacency graph, functional similarity graph, demographic similarity graph, and transportation supply similarity graph to attach spatial dependency to temporal input (i.e., historical demand). The output of GCN is subsequently processed with weather condition information by the Transformer to capture temporal dependency. Then, a convolutional layer is used to generate the final prediction. The proposed model is evaluated for two real-world case studies in Washington, D.C. and Austin, TX, respectively, and the results show that for both case studies, STMGT significantly outperforms all the selected benchmark models, and the most important model component is the weather information. The proposed model can help micromobility operators develop optimal vehicle rebalancing schemes and guide cities to better manage dockless scooter-sharing operations.

Functional brain connectivity indexes derived from low-density EEG of pre-implanted patients as VNS outcome predictors

Objective. In 1/3 of patients, anti-seizure medications may be insufficient, and resective surgery may be offered whenever the seizure onset is localized and situated in a non-eloquent brain region. When surgery is not feasible or fails, vagus nerve stimulation (VNS) therapy can be used as an add-on treatment to reduce seizure frequency and/or severity. However, screening tools or methods for predicting patient response to VNS and avoiding unnecessary implantation are unavailable, and confident biomarkers of clinical efficacy are unclear. Approach. To predict the response of patients to VNS, functional brain connectivity measures in combination with graph measures have been primarily used with respect to imaging techniques such as functional magnetic resonance imaging, but connectivity graph-based analysis based on electrophysiological signals such as electroencephalogram, have been barely explored. Although the study of the influence of VNS on functional connectivity is not new, this work is distinguished by using preimplantation low-density EEG data to analyze discriminative measures between responders and non-responder patients using functional connectivity and graph theory metrics. Main results. By calculating five functional brain connectivity indexes per frequency band upon partial directed coherence and direct transform function connectivity matrices in a population of 37 refractory epilepsy patients, we found significant differences (p < 0.05) between the global efficiency, average clustering coefficient, and modularity of responders and non-responders using the Mann–Whitney U test with Benjamini–Hochberg correction procedure and use of a false discovery rate of 5%. Significance. Our results indicate that these measures may potentially be used as biomarkers to predict responsiveness to VNS therapy.

Time Series Modeling and Forecasting of Drug-Related Deaths in Iran (2014-2016).

Investigating the temporal variations and forecasting the trends in drug-related deaths can help prevent health problems and develop intervention programs. The recent policy in Iran is strongly focused on deterring drug use and replacing illicit drugs with legal ones. This study aimed to investigate drug-related deaths in Iran in 2014-2016 and forecast the death toll by 2019. In this longitudinal study, Box-Jenkins time series analysis was used to forecast drug-related deaths. To this end, monthly counts of drug-related deaths were obtained from March 2014 to March 2017. After data processing, to obtain stationary time series and examine the stability assumption with the Dickey-Fuller test, the parameters of the Autoregressive Integrated Moving Averages (ARIMA) model were determined using autocorrelation function (ACF) and partial autocorrelation function (PACF) graphs. Based on Akaike statistics, ARIMA (0, 1, 1) was selected as the best-fit model. Moreover, the Dickey-Fuller test was used to confirm the stationarity of the time series of transformed observations. The forecasts were made for the next 36 months using the ARIMA (0,1,2) model and the same confidence intervals were applied to all months. The final extracted data were analyzed using R software, Minitab, and SPSS-23. According to the Iranian Ministry of Health and the Legal Medicine Organization, there were 8883 drug-related deaths in Iran from March 2014 to March 2017. According to the time series findings, this count had an upward trend and did not show any seasonal pattern. It was forecasted that the mean drug-related mortality rate in Iran would be 245.8 cases per month until 2019. This study showed a rising trend in drug-related mortality rates during the study period, and the modeling process for forecasting suggested this trend would continue until 2019 if proper interventions were not instituted.

Structural learning of functional directed graphical models with incomplete signals

Functional directed graph model (DGM) learning has been widely used to analyze complex systems. Most existing works assume that the functional signals are complete, which in reality is not true. To address this problem, in this study, a framework for DGM learning with incomplete signals is proposed. Specifically, a penalty term that integrates information from the graph structure is added to the Maximum Margin Matrix Factorization (MMMF) objective function. The proposed method can be used with a known structure to estimate the functional relationship between nodes or with an unknown structure to estimate the relationship together with the graph structure. Numerical experiments and a real-world case study of monocrystalline silicone manufacturing are performed to verify the effectiveness of the proposed method when the signal matrices are incomplete.

Global well‐posedness for the one‐phase Muskat problem

AbstractThe free boundary problem for a two‐dimensional fluid permeating a porous medium is studied. This is known as the one‐phase Muskat problem and is mathematically equivalent to the vertical Hele‐Shaw problem driven by gravity force. We prove that if the initial free boundary is the graph of a periodic Lipschitz function, then there exists a global‐in‐time Lipschitz solution in the strong sense and it is the unique viscosity solution. The proof requires quantitative estimates for layer potentials and pointwise elliptic regularity in Lipschitz domains. This is the first construction of unique global strong solutions for the Muskat problem with initial data of arbitrary size.

Exploring the Neural Processes behind Narrative Engagement: An EEG Study.

Past cognitive neuroscience studies using naturalistic stimuli have considered narratives holistically and focused on cognitive processes. In this study, we incorporated the narrative structure, the dramatic arc, as an object of investigation, to examine how engagement levels fluctuate across a narrative-aligned dramatic arc. We explored the possibility of predicting self-reported engagement ratings from neural activity and investigated the idiosyncratic effects of each phase of the dramatic arc on brain responses as well as the relationship between engagement and brain responses. We presented a movie excerpt following the six-phase narrative arc structure to female and male participants while collecting EEG signals. We then asked this group of participants to recall the excerpt, another group to segment the video based on the dramatic arc model, and a third to rate their engagement levels while watching the movie. The results showed that the self-reported engagement ratings followed the pattern of the narrative dramatic arc. Moreover, while EEG amplitude could not predict group-averaged engagement ratings, other features comprising dynamic intersubject correlation (dISC), including certain frequency bands, dynamic functional connectivity patterns and graph features were able to achieve this. Furthermore, neural activity in the last two phases of the dramatic arc significantly predicted engagement patterns. This study is the first to explore the cognitive processes behind the dramatic arc and its phases. By demonstrating how neural activity predicts self-reported engagement, which itself aligns with the narrative structure, this study provides insights on the interrelationships between narrative structure, neural responses, and viewer engagement.