Graph Of Function Research Articles

PrismParser: A Framework for Implementing Efficient P4-Programmable Packet Parsers on FPGA

The increasing complexity of modern networks and their evolving needs demand flexible, high-performance packet processing solutions. The P4 language excels in specifying packet processing in software-defined networks (SDNs). Field-programmable gate arrays (FPGAs) are ideal for P4-based packet parsers due to their reconfigurability and ability to handle data transmitted at high speed. This paper introduces three FPGA-based P4-programmable packet parsing architectural designs that translate P4 specifications into adaptable hardware implementations called base, overlay, and pipeline, each optimized for different packet parsing performance. As modern network infrastructures evolve, the need for multi-tenant environments becomes increasingly critical. Multi-tenancy allows multiple independent users or organizations to share the same physical network resources while maintaining isolation and customized configurations. The rise of 5G and cloud computing has accelerated the demand for network slicing and virtualization technologies, enabling efficient resource allocation and management for multiple tenants. By leveraging P4-programmable packet parsers on FPGAs, our framework addresses these challenges by providing flexible and scalable solutions for multi-tenant network environments. The base parser offers a simple design for essential packet parsing, using minimal resources for high-speed processing. The overlay parser extends the base design for parallel processing, supporting various bus sizes and throughputs. The pipeline parser boosts throughput by segmenting parsing into multiple stages. The efficiency of the proposed approaches is evaluated through detailed resource consumption metrics measured on an Alveo U280 board, demonstrating throughputs of 15.2 Gb/s for the base design, 15.2 Gb/s to 64.42 Gb/s for the overlay design, and up to 282 Gb/s for the pipelined design. These results demonstrate a range of high performances across varying throughput requirements. The proposed approach utilizes a system that ensures low latency and high throughput that yields streaming packet parsers directly from P4 programs, supporting parsing graphs with up to seven transitioning nodes and four connections between nodes. The functionality of the parsers was tested on enterprise networks, a firewall, and a 5G Access Gateway Function graph.

Functional Connectivity and Graph Embedding-Based Domain Adaptation for Autism Classification from Multi-site Data

Functional Connectivity and Graph Embedding-Based Domain Adaptation for Autism Classification from Multi-site Data

Expressing Distance in Graphs of Functions in the Cartesian Plane: Obstacles and Interventions

Expressing Distance in Graphs of Functions in the Cartesian Plane: Obstacles and Interventions

The Past and Future of Aesthetics in Mathematics

This paper explores the connotations of mathematical aesthetics and its connections with art, facilitated by collaboration with Ester, an individual with an artistic professional background. It begins by tracing the historical evolution of aesthetics from the classical pursuit of authenticity to the modern shift toward self-expression in art. The discussion then highlights the similarities in the pursuit of truth between mathematics and art, despite their methodological differences. Through an analysis of aesthetic elements in mathematics, such as lines and function graphs, the article illustrates that the beauty of mathematics is not only manifested in cognitive processes but can also be intuitively expressed through visual arts. The paper further examines the influence of mathematics on the development of art, particularly how Leonardo da Vinci applied mathematical principles to his artworks. Additionally, the article addresses art students’ perceptions of mathematics, proposes the customization of math courses for art students, and discusses future trends in the integration of mathematics and art, emphasizing the significance of art therapy and the altruistic direction of art. Lastly, the authors use a poster to visually convey the idea that the beauty of mathematics can be experienced through the senses.

SmartExecutor: Coverage-Driven Symbolic Execution Guided via State Prioritization and Function Selection

Symbolic execution of smart contracts suffers from sequence explosion. Some existing tools limit the sequence length, thus being unable to adequately evaluate some functions. In this paper, we propose a symbolic execution approach without limiting the sequence length. In our approach, the symbolic execution process is a two-phase model that maximizes code coverage while reducing the number of sequences to be executed. The first phase executes all sequences up to a length limit to identify the not-fully covered functions while the second attempts to cover these functions according to state evaluation and a function graph structure. We have developed a tool called SmartExecutor and conducted an experimental evaluation on the SGUARD dataset. The experimental results indicate that compared with state-of-the-art tools, SmartExecutor achieves higher code coverage with less time. It also detects more vulnerabilities than Mythril, a state-of-the-art symbolic execution tool.

A Hierarchical Graph Neural Network Framework for Predicting Protein-Protein Interaction Modulators With Functional Group Information and Hypergraph Structure.

Accurate prediction of small molecule modulators targeting protein-protein interactions (PPIMs) remains a significant challenge in drug discovery. Existing machine learning-based models rely on manual feature engineering, which is tedious and task-specific. Recently, deep learning models based on graph neural networks have made remarkable progress in molecular representation learning. However, many graph-based approaches ignore molecular hierarchical structure modeling guided by domain knowledge. In chemistry, the functional groups of a molecule determine its interaction with specific targets. Therefore, we propose a hierarchical graph neural network framework (called HiGPPIM) for predicting PPIMs by integrating atom-level and functional group-level features of molecules. HiGPPIM constructs atom-level and functional group-level graphs based on chemical knowledge and learns graph representations using graph attention networks. Furthermore, a hypergraph attention network is designed in HiGPPIM to aggregate and transform two-level graph information. We evaluate the performance of HiGPPIM on eight PPI families and two prediction tasks, namely PPIM identification and potency prediction. Experimental results demonstrate that HiGPPIM achieves state-of-the-art performance on both tasks and that using functional group information to guide PPIM prediction is effective.

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.