Graph Of Function Research Articles

A Region-Monitoring-Type Slitless Imaging Spectrometer.

In modern scientific practice, it is necessary to consistently observe predetermined zones, with the expectation of detecting and identifying emerging targets or events inside such areas. This research presents an innovative imaging spectrometer system for the continuous monitoring of specific areas. This study begins by providing detailed information on the features and optical structure of the constructed instrument. This is then followed by simulations using optical design tools. The device has an F-number of 5, a focal length of 100 mm, a field of view of 3 × 7, and a wavelength range spanning from 400 nm to 600 nm. The optical path diagram demonstrates that the system's dispersion and imaging pictures can be distinguished, hence fulfilling the system's specifications. Furthermore, the utilization of a Modulation Transfer Function (MTF) graph has substantiated that the image quality indeed satisfies the specified criteria. To evaluate the instrument's performance in the spectrum observation of fixed regions, a region-monitoring-type slitless imaging spectrometer was built. The equipment has the capability to identify a specific region and rapidly capture the spectra of objects or events that are present inside that region. The spectral data were collected effectively by the implementation of image processing techniques on the captured photos. The correlation coefficient between these data and the reference data was 0.9226, showing that the device successfully measured the target's spectrum. Therefore, the instrument that was created successfully demonstrated its ability to capture images of the observed areas and collect spectral data from the targets located within those regions.

Asymmetric Effects of Economic Growth, Fossil Fuel Consumption, and Financial Development on Carbon Emissions in Ghana

This research analyzes the impact of economic expansion, non-renewable energy consumption (NonREC), financial sector improvement, and carbon releases in Ghana. The study used yearly data from 1971 to 2014 and applied the Nonlinear Autoregressive Distributed Lag (NARDL) method to examine the data. The NARDLapproach facilitated the differentiation of variables into favorable and unfavorable adjustments by examining the short- and long-run effects. The results indicated that all the independent variables exhibited short-term asymmetries, while economic growth presented long-term asymmetry. Negative adjustments in economic expansion led to a decline in carbon releases in the long run but an increase in the short run. favorable and unfavorable adjustments in NonREC positively and negatively impact carbon releases in both the short and long term. Additionally, negative adjustments in financial development positively affected carbon releases in the long run. The cumulative dynamic multipliers graphs and impulse response function graphs illustrate the same impact pattern of the independent variables on carbon releases, confirming the findings' robustness. The study suggests implementing environmental policies in Ghana that promote renewable sources of energy and energy-conserving innovations to reduce environmental degradation. The findings recommend that the decision-maker prioritize effective environmental strategies like a green economy, renewable energy use, and energy-saving technologies. By adopting clean energy and implementing advanced technologies, sustainable economic growth can be achieved while preserving the environment and the ecosystem.

A deep learning framework for predicting disease-gene associations with functional modules and graph augmentation

BackgroundThe exploration of gene-disease associations is crucial for understanding the mechanisms underlying disease onset and progression, with significant implications for prevention and treatment strategies. Advances in high-throughput biotechnology have generated a wealth of data linking diseases to specific genes. While graph representation learning has recently introduced groundbreaking approaches for predicting novel associations, existing studies always overlooked the cumulative impact of functional modules such as protein complexes and the incompletion of some important data such as protein interactions, which limits the detection performance.ResultsAddressing these limitations, here we introduce a deep learning framework called ModulePred for predicting disease-gene associations. ModulePred performs graph augmentation on the protein interaction network using L3 link prediction algorithms. It builds a heterogeneous module network by integrating disease-gene associations, protein complexes and augmented protein interactions, and develops a novel graph embedding for the heterogeneous module network. Subsequently, a graph neural network is constructed to learn node representations by collectively aggregating information from topological structure, and gene prioritization is carried out by the disease and gene embeddings obtained from the graph neural network. Experimental results underscore the superiority of ModulePred, showcasing the effectiveness of incorporating functional modules and graph augmentation in predicting disease-gene associations. This research introduces innovative ideas and directions, enhancing the understanding and prediction of gene-disease relationships.

SKAFFOLDING TECHNIQUE IN GRAPHING ELEMENTARY FUNCTIONS – A CASE STUDY

<p>In this paper, the authors present the application of the scaffolding technique in drawing graphs of some elementary functions. First-year students of the Faculty of Architecture, Civil Engineering, and Geodesy were tested using two exams: an entrance test and an exit test. The obtained results show whether students are more successful in drawing graphs of elementary functions after using the scaffolding technique in math teaching. Based on the research results, scaffolding can indeed help students in graphing elementary functions.</p>

Box dimension of harmonic functions on higher dimensional Sierpinski gasket and Sierpinski gasket with bilateral energy

This paper concentrates on the bounds of the box-counting dimension of the graph of various fractal functions on the (N-1) dimensional Sierpinski gasket for N≥3. The bounds of the box-counting dimension of the graph of harmonic functions and functions having finite energy associated with the standard self-similar energy are found. Besides that, the bounds for the graph of harmonic functions and functions having finite energy associated with the bilateral energy on the Sierpinski gasket are also examined.

Development of the GeoGebra’s Guidebook in Creating Mathematics Learning Media Based on Ethnomathematics

This research aims to develop a guidebook for the use of GeoGebra in creating mathematics learning media based on ethnomathematics for university students in mathematics education study program at Pattimura University PSDKU Maluku Barat Daya. The method used in this research is Research and Development (R&D) with 4D model developed by Thiagarajan et al. (1974) which consists of 4 stages, namely Define, Design, Develop and Disseminate. This method and model are very feasible and systematically supports the development of the guidebook. By involving 2 validators, namely material experts and linguists, the draft of the guidebook was then revised and tested on a small limited group. Furthermore, based on descriptive statistical analysis and qualitative descriptive analysis, it can be concluded that the reference book using GeoGebra has been successfully prepared and meets the criteria of valid and effective. In addition, the use of this guidebook can also increase students' knowledge in understanding material related to cartesian coordinates, especially in drawing graphs of linear functions, quadratic functions, polynomials, trigonometric functions, exponent functions, and logarithms.

Oscillation-Specific Nodal Differences in Parkinson's Disease Patients with Anxiety.

Parkinson's disease (PD) is a common neurodegenerative disorder that is predominantly known for its motor symptoms but is also accompanied by non-motor symptoms, including anxiety. The underlying neurobiological substrates and brain network changes associated with comorbid anxiety in PD require further exploration. An analysis of oscillation-specific nodal properties in patients with and without anxiety was conducted using resting-state functional magnetic resonance imaging (rs-fMRI) and graph theory. We used a band-pass filtering approach to differentiate oscillatory frequency bands for subsequent functional connectivity (FC) and graph analyses. The study included 68 non-anxiety PD (naPD) patients, 62 anxiety PD (aPD) patients, and 64 healthy controls (NC). Analyses of nodal betweenness centrality (BC), degree centrality (DC), and efficiency were conducted across multiple frequency bands. The findings indicated no significant differences in BC among naPD, aPD, and NC within the 0.01-0.08 Hz frequency range. However, we observed a specific reduction in BC at narrower frequency ranges in aPD patients, as well as differing patterns of change in DC and efficiency, which are believed to reflect the neurophysiological bases of anxiety symptoms in PD. Differential oscillation-specific nodal characteristics have been identified in PD patients with anxiety, suggesting potential dysregulations in brain network dynamics. These findings emphasize the complexity of brain network alterations in anxiety-associated PD and identify oscillatory frequencies as potential biomarkers. The study highlights the importance of considering oscillatory frequency bands in the analysis of brain network changes.

THE TECHNOLOGY OF TEACHING THE GRAPHS OF SOME ELEMENTARY FUNCTIONS IN THE SCHOOL MATHEMATICS COURSE FOR GRADES VII-IX

The understanding of functions and the requirements associated with them in the school mathematics course has found sufficient reflection in the curriculum, emphasizing its significant importance. This point is discussed in the article, where some elementary functions and their teaching methodology are explained based on modern teaching technologies. Graphs of certain elementary functions in grades VII-IX are constructed using concrete examples.

Abnormal brain functional network dynamics in amyotrophic lateral sclerosis patients with depression.

Since depression is common in amyotrophic lateral sclerosis (ALS) patients, we aimed to explore the specific brain functional network dynamics in ALS patients with depression (ALS-D) compared with healthy controls (HCs) and ALS patients without depressive symptoms (ALS-ND). According to the DSM-V, 32 ALS-D patients were selected from a large and newly diagnosed ALS cohort. Then, 32 demographic- and cognitive-matched ALS-ND patients were also selected, and 64 HCs were recruited. These participants underwent resting-state fMRI scans, and functional connectivity state analysis and dynamic graph theory were applied to evaluate brain functional network dynamics. Moreover, the Hamilton Depression Rating Scale (HDRS) was used to quantify depressive symptoms in the ALS-D patients. Four distinct states were identified in the ALS-D patients and controls. Compared with that in HCs, the fraction rate (FR) in state 2 was significantly decreased in ALS-D patients, and the FR in state 4 was significantly increased in ALS-D patients. Compared with that of HCs, the dwell time in state 4 was significantly increased in the ALS-D patients. Moreover, compared with that in the ALS-D patients, the FR in state 3 was significantly decreased in the ALS-ND patients. Among the ALS-D patients, there was the suggestion of a positive association between HDRS scores and dwell time of state 4, but this association did not reach statistical significance (r = 0.354; p = 0.055). Depression is an important feature of ALS patients, and we found a special pattern of brain functional network dynamics in ALS-D patients. Our findings may play an important role in understanding the mechanism underlying depression in ALS patients and help develop therapeutic interventions for depressed ALS patients.

A novel metaheuristic optimization and soft computing techniques for improved hydrological drought forecasting

Drought is one of the costliest natural disasters worldwide and weakens countries economically by causing negative impacts on hydropower and agricultural production. Therefore, it is necessary to create drought risk management plans by monitoring and predicting droughts. Various drought indicators have been developed to monitor droughts. This study aims to forecast Streamflow Drought Index (SDI) values with various novel metaheuristic optimization-based Artificial Neural Network (ANN) and deep learning models to predict 1-month lead-time hydrological droughts on 1, 3, and 12-month time scales in the Konya closed basin, one of the driest basins in Turkey. To achieve this goal, the ANN model was integrated with the Firefly Algorithm (FFA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) techniques and compared against long short-term memory (LSTM) networks. While establishing the SDI prediction model, lag values exceeding the 95% confidence intervals in the partial autocorrelation function graphs were used. Model performance was evaluated according to scatter matrix, radar, time series, bee swarm graphs, and statistical performance metrics. As a result of the analysis, the PSO-ANN hybrid model with (R2:0.468–0.931) at station 1611 and the FFA-ANN hybrid model with (R2:0.443–0.916) at station 1612 generally have the highest accuracy.

Extension of Synthetic Division and Its Applications

This study focused on \enquote{Extension of synthetic division and its applications}. The study was designed to show synthetic division and its extension and to point out the applications of synthetic division and its extension. The study found out that the concepts of polynomial and rational expressions in single variables are basic concepts to deal extension of synthetic division and its applications. Using the preliminary concepts, the concept of synthetic division is extended in this study. Also, the study found out that an extension of synthetic division is used for finding the oblique asymptote of the graph of a rational function, evaluating the integration of some rational functions, representing polynomial expression by factorial function in numerical analysis, and so on.

Impact of warranty and green level of the product with nonlinear demand via optimal control theory and Artificial Hummingbird Algorithm

Due to the current environmental situation and human health, a green manufacturing system is very essential in the manufacturing world. Several researchers have developed various types of green manufacturing models by considering green products, green investments, carbon emission taxes, etc. Motivated by this topic, a green production model is formulated by considering selling price, time, warranty period and green level dependent demand with a carbon emission tax policy. Also, the production rate of the system is an unknown function of time. Per unit production cost of the products is taken as increasing function of production rate and green level of the products. In our proposed model, carbon emission rate is taken as linear function of time. Then, an optimization problem of the production model is constructed. To validate of our proposed model, a numerical example is considered and solved it by AHA. Further, other five metaheuristics algorithms (AEFA, FA, GWOA, WOA and EOA) are taken to compare the results obtained from AHA. Also, concavity of the average profit function and convergence graph of different metaheuristics algorithms are presented. Finally, a sensitivity analysis is carried out to investigate the impact of different system parameters on our optimal policy and reach a fruitful conclusion from this study.

Study on Sustainability of Property Insurance

This paper is about developing and applying insurance models for historic landmarks that are in locations that experience extreme weather events. In order to make it,we devided this whole problem into 2 Questions as followed. Question 1 is about developing an insurance model for property owners and developers in areas that experience extreme weather events.The model has considered the risk level, feasibility, and desirability of the insurance, and use the Bayesian graph, maximum likelihood distribution, function graph, and entropy weight method to construct and evaluate the model.Question 2 is about applying the insurance model to a specific case study, which is the Cape Hatteras Lighthouse in North Carolina. We’ve assessed the value of the lighthouse, and compare and contrast the insurance options for the lighthouse before and after the relocation.All in all, the paper demonstrates the models using the Cape Hatteras Lighthouse as case study, and provides some results, implications, and recommendations for the stakeholders.

Developing Functional Thinking: from Concrete to Abstract Through an Embodied Design

AbstractIn addressing the challenge of fostering functional thinking (FT) in secondary school students, our research centered on the question of how an embodied design can enhance FT’s different aspects, including input–output, covariation, and correspondence views. Drawing from embodied cognition theory and focusing on an action- and perception-based task design that uses light ray contexts and different function representations, we developed a digital-embodied learning environment, using the nomogram as a central representation. Our pilot study involving four eighth-grade students provided insights into their physical interactions with these modules through a multi-touch digital interface. Analysis of video and audio recordings from the pilots, including students’ hand gestures and verbal expressions, was guided by comparing hypothetical learning activities with the actual learning activities. The results show that (1) a concrete light ray context enables students to ground the abstract mathematical function concept; (2) the bimanual coordinating motion tasks, incorporating the covariation aspect of FT, allow students to connect their bodily experience with function properties; and (3) our embodied and dragging tasks support insight in the conversion between nomograms and graphs of functions, encouraging students’ correspondence thinking by providing multiple perspectives to understand, reason about, and manipulate the function. In conclusion, our findings suggest the potential of digital-embodied tasks in fostering FT, evident in students’ diverse strategies and reasoning.

On the dimensional connection between a class of real number sequences and local fractal functions with a single unbounded variation point

In this paper, we investigate the connection between a class of real number sequences and local fractal functions in terms of fractal dimensions. Under certain conditions, we show that the Box dimension of the graph of a local fractal function with a single unbounded variation point is equal to that of its zero points set plus one. Several concrete examples of such functions whose Box dimension can take any numbers belonging to [1,2] have also been given. This work may provide new approaches to the construction of various local fractal functions with the required Box dimension in the future.

Graph Theory Further Revealed Visual Spatial Working Memory Impairment in Patients with Inflammatory Bowel Disease.

Inflammatory Bowel Disease (IBD) patients may experience cognitive impairments in Visuospatial Working Memory (VSWM), significantly impacting their quality of life. However, the mechanisms underlying these impairments remain poorly understood. We studied functional MRI and graph theory analysis to investigate changes in functional connectivity networks during the Mental Rotation Task (MRT) in IBD patients. Twenty IBD patients (13 males, 7 females; mean age = 34.95 ± 13.80 years; mean disease duration = 2.43 ± 2.37 years) participated in the study. Exclusion criteria encompassed recent use of analgesics, 5-Aminosalicylate, corticosteroids, or immunosuppressants within the past three months. Additionally, we recruited 20 age-, gender-, and education-matched healthy controls for comparison. Compared to a control group, IBD patients exhibited significantly longer reaction times and reduced accuracy during the MRT. Our analysis revealed abnormalities in multiple nodal attributes within the functional connectivity network, particularly in regions such as the bilateral orbitofrontal cortex, right supplementary motor area, bilateral parahippocampal gyrus, and bilateral anterior temporal lobe. We observed that the nodal efficiency in the left temporal pole is negatively correlated with Red Blood Cell Distribution Width (RDW) and positively correlated with response time of MRT. Our findings revealed notable abnormalities in multiple node attributes among IBD patients during MRT, providing evidence of cognitive impairments in VSWM in IBD patients. This study found RDW maybe can serve as a clinical indicator for predicting early VSWM impairment in patients with IBD.

THE DEVELOPMENT OF MATHEMATICS LEARNING ACHIEVEMENT ON THE TOPIC OF SOLVING QUADRATIC FUNCTION GRAPHS OF MATHAYOM 3 STUDENTS BY USING THE GEOGEBRA PROGRAM TOGETHER WITH POLYA'S PROBLEM SOLVING PROCESS

This research used GeoGebra program and organized learning management activities in accordance with Polya’s problem-solving process to develop mathematical learning achievement by solving problems in quadratic function graphs. With the help of GeoGebra program and step-by-step practice of problem-solving techniques using Polya’s problem-solving process, the aforementioned learning management system increases students' enthusiasm and interest in learning about graphs. Consequently, it encourages students to comprehend the knowledge of quadratic function graphs in mathematics efficiently, gain a more thorough comprehension of them, and develop their skills in solving problems. The target group used in the research is 14 Mathayom 3 students studying in the first semester of the academic year 2023 at Chumchonyodkaengsongkhro School, Namon District, Kalasin Province, which obtained purposive random sampling. The tools used in the research were lesson plans using GeoGebra with Polya’s problem-solving process, learning achievement tests, and a satisfaction questionnaire. The statistics used in the data analysis include mean (x̄), standard deviation (SD), percentage, and t-test statistics. The results of the research found that: 1) the results of the efficiency of the lesson plans using GeoGebra program with Polya’s problem solving process are equal to 73.75/74.64, which is higher than with the specified criteria, 2) The post-test scores’ learning achievement using GeoGebra with Polya's problem-solving process was higher than the pre-test scores using GeoGebra with Polya's problem-solving process, with statistical significance at the .05 level, and 3) the satisfaction of students with learning management using GeoGebra program with Polya’s problem-solving process is at a high level with an average of 4.31 and a standard deviation of 0.81.

Chemoembolization for Hepatocellular Carcinoma Including Contrast Agent-Enhanced CT: Response Assessment Model on Radiomics and Artificial Intelligence

Purpose: The aim of this study was to assess the efficacy of an artificial intelligence (AI) algorithm that uses radiomics data to assess recurrence and predict survival in hepatocellular carcinoma (HCC) treated with transarterial chemoembolization (TACE). Methods: A total of 57 patients with treatment-naïve HCC or recurrent HCC who were eligible for TACE were prospectively enrolled in this study as test data. A total of 100 patients with treatment-naïve HCC or recurrent HCC who were eligible for TACE were retrospectively acquired for training data. Radiomic features were extracted from contrast-enhanced, liver computed tomography (CT) scans obtained before and after TACE. An AI algorithm was trained using the retrospective data and validated using the prospective test data to assess treatment outcomes. Results: This study evaluated 107 radiomic features and 5 clinical characteristics as potential predictors of progression-free survival and overall survival. The C-index was 0.582 as the graph of the cumulative hazard function, predicted by the variable configuration by using 112 radiomics features. The time-dependent AUROC was 0.6 ± 0.06 (mean ± SD). Among the selected radiomics features and clinical characteristics, baseline_glszm_SizeZoneNonUniformity, baseline_ glszm_ZoneVariance and tumor size had excellent performance as predictors of HCC response to TACE with AUROC of 0.853, 0.814 and 0.827, respectively. Conclusions: A radiomics-based AI model is capable of evaluating treatment outcomes for HCC treated with TACE.

Insight into soft chemometric computational learning for modelling oily-wastewater separation efficiency and permeate flux of polypyrrole-decorated ceramic-polymeric membranes

Reliable modeling of oily wastewater emphasizes the paramount importance of sustainable and health-conscious wastewater management practices, which directly aligns with the Sustainable Development Goals (SDG) while also meeting the guidelines of the World Health Organization (WHO). This research explores the efficiency of utilizing polypyrrole-coated ceramic-polymeric membranes to model oily wastewater separation efficiency (SE) and permeate flux (PF) based on established experimental procedures. In this area, computational simulation still needs to be explored. The study developed predictive regression models, including robust linear regression (RLR), stepwise linear regression (SWR) and linear regression (LR) for the ceramic-polymeric porous membrane, aiming to interpret its complex performance across diverse conditions and, thus, develop its utility in oily wastewater treatment applications. Subsequently, a novel, simple average ensemble paradigm was explored to reduce errors and improve prediction skills. Prior to the development of the model, stability and reliability analysis of the data was conducted based on Philip Perron tests with the Bartlett kernel estimation method. The accuracy of the SE exhibited a high consistency, averaging 99.92% with minimal variability (standard deviation of 0.026%), potentially simplifying its prediction compared to PF. The modes were validated and evaluated using metrics like MAE, RMSE, Speed, and MSE, in addition to 2D graphical and cumulative distribution function graphs. The LR model emerged as the best with the lowest RMSE =0.21951, indicating superior prediction accuracy, followed closely by RLR with an RMSE = 0.22359. SWLR, while having the highest RMSE = 0.34573, marked its dominance in prediction speed with 110 observations per second. Notably, the RLR model justified a reduction in error by approximately 35.29% compared to SWLR. Moreover, the training efficiency of the LR model exceeded, demanding a mere 2.9252 s, marking a reduction of about 32.54% compared to SWLR. The improved simple ensemble learning proved merit over the three models regarding error accuracy. This study emphasizes the essential role of soft-computing learning in optimizing the design and performance of ceramic-polymeric membranes.

280 Enhancing Nephrology Care Access: Development and Implementation of a Telenephrology Dashboard Through Human-Centered Design

OBJECTIVES/GOALS: Our objective is to develop a Telenephrology dashboard for the 150,000 Veterans that obtain care through the Iowa City Veterans Affairs Health Care System. Our goal is to create a comprehensive and user-friendly tool for monitoring kidney health and facilitating remote nephrology consultations. METHODS/STUDY POPULATION: We structured our intervention according to the five stages of human-centered design: (1) Empathize, (2) Define, (3) Ideate, (4) Prototype and (5) Test. During the empathy stage, the principal investigator spent 10 hours immersed in the clinical setting observing how nephrologists approach a remote nephrology consultation. These observations were augmented by unstructured interviews with clinicians and patients to better understand the process and dynamics. Following this, a rapid ideation workshop was convened to generate creative solutions that balance technical requirements with the needs of clinicians and patients. These led to rapid prototyping and testing to identify what elements of the prototypes worked and which needed improvement. RESULTS/ANTICIPATED RESULTS: Through the empathy and define stages, three needs were identified: (1) clarity in visualizing data, (2) accuracy of information, and (3) balancing standardization with individualization. During the rapid ideation workshop, the concept of a four-frame dashboard was settled upon. This led to the creation of five prototypes, which were tested. These were reconciled and modified to make a final product. This final product, the Telenephrology Dashboard, contains 5 elements that support nephrologists and supporting staff: (1) a graph of kidney function over time, (2) tables synthesizing lab data, (3) options to drill down events to specific times, (4) customization of views, and (5) integration of kidney disease progression models. DISCUSSION/SIGNIFICANCE: A Telenephrology dashboard was created to facilitate remote nephrology consultations through a Human-Centered Design process. Our next steps include determining if this dashboard may improve end-user satisfaction, referring clinician satisfaction, access to specialist care, and patient outcomes.