Search results for: isomorphism of graph

Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

Keywords: Malfatti’s problem, geometric constraint solver, computer-aided geometric design, circle packing, data visualization

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Authors: Simeon Mayala, Ida Herdlevær, Jonas Bull Haugsøen, Shamundeeswari Anandan, Sonia Gavasso, Morten Brun

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In this paper, we propose a minimum spanning tree-based method for segmenting brain tumors. The proposed method performs interactive segmentation based on the minimum spanning tree without tuning parameters. The steps involve preprocessing, making a graph, constructing a minimum spanning tree, and a newly implemented way of interactively segmenting the region of interest. In the preprocessing step, a Gaussian filter is applied to 2D images to remove the noise. Then, the pixel neighbor graph is weighted by intensity differences and the corresponding minimum spanning tree is constructed. The image is loaded in an interactive window for segmenting the tumor. The region of interest and the background are selected by clicking to split the minimum spanning tree into two trees. One of these trees represents the region of interest and the other represents the background. Finally, the segmentation given by the two trees is visualized. The proposed method was tested by segmenting two different 2D brain T1-weighted magnetic resonance image data sets. The comparison between our results and the standard gold segmentation confirmed the validity of the minimum spanning tree approach. The proposed method is simple to implement and the results indicate that it is accurate and efficient.

Keywords: brain tumor, brain tumor segmentation, minimum spanning tree, segmentation, image processing

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Authors: Hui-Chuan Lu

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In a perfect secret-sharing scheme, a dealer distributes a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of the participants in any unqualified subset is statistically independent of the secret. The access structure of the scheme refers to the collection of all qualified subsets. In a graph-based access structures, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme realizing a given access structure is the ratio of the average length of the shares given to the participants to the length of the secret. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing an access structure is called the optimal average information ratio of that access structure. We study the optimal average information ratio of the access structures based on bipartite graphs. Based on some previous results, we give a bound on the optimal average information ratio for all bipartite graphs of girth at least six. This bound is the best possible for some classes of bipartite graphs using our approach.

Keywords: secret-sharing scheme, average information ratio, star covering, deduction, core cluster

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Authors: Chia-Feng Lu, Yuh-Jen Wang, Shin Teng, Yu-Te Wu, Sui-Hing Yan

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Brain functional networks based on resting-state EEG data were compared between patients with mild Alzheimer’s disease (mAD) and matched patients with amnestic subtype of mild cognitive impairment (aMCI). We integrated the time–frequency cross mutual information (TFCMI) method to estimate the EEG functional connectivity between cortical regions and the network analysis based on graph theory to further investigate the alterations of functional networks in mAD compared with aMCI group. We aimed at investigating the changes of network integrity, local clustering, information processing efficiency, and fault tolerance in mAD brain networks for different frequency bands based on several topological properties, including degree, strength, clustering coefficient, shortest path length, and efficiency. Results showed that the disruptions of network integrity and reductions of network efficiency in mAD characterized by lower degree, decreased clustering coefficient, higher shortest path length, and reduced global and local efficiencies in the delta, theta, beta2, and gamma bands were evident. The significant changes in network organization can be used in assisting discrimination of mAD from aMCI in clinical.

Keywords: EEG, functional connectivity, graph theory, TFCMI

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Authors: Patrick Cummings, Laura Cassani, Deirdre Kelliher

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In this paper we present findings from a research effort to apply a hybrid collaborative-context approach for a system focused on Marine Corps civil affairs data collection, aggregation, and analysis called the Marine Civil Information Management System (MARCIMS). The goal of this effort is to provide operators with information to make sense of the interconnectedness of entities and relationships in their area of operation and discover existing data to support civil military operations. Our approach to build a recommendation engine was designed to overcome several technical challenges, including 1) ensuring models were robust to the relatively small amount of data collected by the Marine Corps civil affairs community; 2) finding methods to recommend novel data for which there are no interactions captured; and 3) overcoming confirmation bias by ensuring content was recommended that was relevant for the mission despite being obscure or less well known. We solve this by implementing a combination of collective matrix factorization (CMF) and graph-based random walks to provide recommendations to civil military operations users. We also present a method to resolve the challenge of computation complexity inherent from highly connected nodes through a precomputed process.

Keywords: Recommendation engine, collaborative filtering, context based recommendation, graph analysis, coverage, civil affairs operations, Marine Corps

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Authors: Pallavi Bhogaram, Xiaolong Wu, Min He, Onyedikachi Okenwa

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A transportation network is a realization of a spatial network, describing a structure which permits either vehicular movement or flow of some commodity. Examples include road networks, railways, air routes, pipelines, and many more. The transportation network plays a vital role in maintaining the vigor of the nation’s economy. Hence, ensuring the network stays resilient all the time, especially in the face of challenges such as heavy traffic loads and large scale natural disasters, is of utmost importance. In this paper, we used the Neo4j application to develop the graph. Neo4j is the world's leading open-source, NoSQL, a native graph database that implements an ACID-compliant transactional backend to applications. The Southern California network model is developed using the Neo4j application and obtained the most critical and optimal nodes and paths in the network using centrality algorithms. The edge betweenness centrality algorithm calculates the critical or optimal paths using Yen's k-shortest paths algorithm, and the node betweenness centrality algorithm calculates the amount of influence a node has over the network. The preliminary study results confirm that the Neo4j application can be a suitable tool to study the important nodes and the critical paths for the major congested metropolitan area.

Keywords: critical path, transportation network, connectivity reliability, network model, Neo4j application, edge betweenness centrality index

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Authors: Ali Kazemi

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Those within the volatile and interconnected international economic markets, appropriately predicting market trends, hold substantial fees for traders and financial establishments. Traditional device mastering strategies have made full-size strides in forecasting marketplace movements; however, monetary data's complicated and networked nature calls for extra sophisticated processes. This observation offers a groundbreaking method for monetary marketplace prediction that leverages the synergistic capability of Graph Convolutional Networks (GCNs) and Long Short-Term Memory (LSTM) networks. Our suggested algorithm is meticulously designed to forecast the traits of inventory market indices and cryptocurrency costs, utilizing a comprehensive dataset spanning from January 1, 2015, to December 31, 2023. This era, marked by sizable volatility and transformation in financial markets, affords a solid basis for schooling and checking out our predictive version. Our algorithm integrates diverse facts to construct a dynamic economic graph that correctly reflects market intricacies. We meticulously collect opening, closing, and high and low costs daily for key inventory marketplace indices (e.g., S&P 500, NASDAQ) and widespread cryptocurrencies (e.g., Bitcoin, Ethereum), ensuring a holistic view of marketplace traits. Daily trading volumes are also incorporated to seize marketplace pastime and liquidity, providing critical insights into the market's shopping for and selling dynamics. Furthermore, recognizing the profound influence of the monetary surroundings on financial markets, we integrate critical macroeconomic signs with hobby fees, inflation rates, GDP increase, and unemployment costs into our model. Our GCN algorithm is adept at learning the relational patterns amongst specific financial devices represented as nodes in a comprehensive market graph. Edges in this graph encapsulate the relationships based totally on co-movement styles and sentiment correlations, enabling our version to grasp the complicated community of influences governing marketplace moves. Complementing this, our LSTM algorithm is trained on sequences of the spatial-temporal illustration discovered through the GCN, enriched with historic fee and extent records. This lets the LSTM seize and expect temporal marketplace developments accurately. Inside the complete assessment of our GCN-LSTM algorithm across the inventory marketplace and cryptocurrency datasets, the version confirmed advanced predictive accuracy and profitability compared to conventional and opportunity machine learning to know benchmarks. Specifically, the model performed a Mean Absolute Error (MAE) of 0.85%, indicating high precision in predicting day-by-day charge movements. The RMSE was recorded at 1.2%, underscoring the model's effectiveness in minimizing tremendous prediction mistakes, which is vital in volatile markets. Furthermore, when assessing the model's predictive performance on directional market movements, it achieved an accuracy rate of 78%, significantly outperforming the benchmark models, averaging an accuracy of 65%. This high degree of accuracy is instrumental for techniques that predict the course of price moves. This study showcases the efficacy of mixing graph-based totally and sequential deep learning knowledge in economic marketplace prediction and highlights the fee of a comprehensive, records-pushed evaluation framework. Our findings promise to revolutionize investment techniques and hazard management practices, offering investors and economic analysts a powerful device to navigate the complexities of cutting-edge economic markets.

Keywords: financial market prediction, graph convolutional networks (GCNs), long short-term memory (LSTM), cryptocurrency forecasting

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Authors: Zhipeng Chen, Peng Zhang, Qingyun Liu, Li Guo

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With the Internet becoming the dominant channel for business and life, many IPs are increasingly masked using web proxies for illegal purposes such as propagating malware, impersonate phishing pages to steal sensitive data or redirect victims to other malicious targets. Moreover, as Internet traffic continues to grow in size and complexity, it has become an increasingly challenging task to detect the proxy service due to their dynamic update and high anonymity. In this paper, we present an approach based on behavioral graph analysis to study the behavior similarity of web proxy users. Specifically, we use bipartite graphs to model host communications from network traffic and build one-mode projections of bipartite graphs for discovering social-behavior similarity of web proxy users. Based on the similarity matrices of end-users from the derived one-mode projection graphs, we apply a simple yet effective spectral clustering algorithm to discover the inherent web proxy users behavior clusters. The web proxy URL may vary from time to time. Still, the inherent interest would not. So, based on the intuition, by dint of our private tools implemented by WebDriver, we examine whether the top URLs visited by the web proxy users are web proxies. Our experiment results based on real datasets show that the behavior clusters not only reduce the number of URLs analysis but also provide an effective way to detect the web proxies, especially for the unknown web proxies.

Keywords: bipartite graph, one-mode projection, clustering, web proxy detection

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Authors: Mubarack Ahmed, Gabriele Gradoni, Stephen C. Creagh, Gregor Tanner

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High-frequency cables commonly connect modern devices and sensors. Interestingly, the proportion of electric components is rising fast in an attempt to achieve lighter and greener devices. Modelling the propagation of signals through these cable networks in the presence of parameter uncertainty is a daunting task. In this work, we study the response of high-frequency cable networks using both Transmission Line and Quantum Graph (QG) theories. We have successfully compared the two theories in terms of reflection spectra using measurements on real, lossy cables. We have derived a generalisation of the vertex scattering matrix to include non-uniform networks – networks of cables with different characteristic impedances and propagation constants. The QG model implicitly takes into account the pseudo-chaotic behavior, at the vertices, of the propagating electric signal. We have successfully compared the asymptotic growth of eigenvalues of the Laplacian with the predictions of Weyl law. We investigate the nearest-neighbour level-spacing distribution of the resonances and compare our results with the predictions of Random Matrix Theory (RMT). To achieve this, we will compare our graphs with the generalisation of Wigner distribution for open systems. The problem of scattering from networks of cables can also provide an analogue model for wireless communication in highly reverberant environments. In this context, we provide a preliminary analysis of the statistics of communication capacity for communication across cable networks, whose eventual aim is to enable detailed laboratory testing of information transfer rates using software defined radio. We specialise this analysis in particular for the case of MIMO (Multiple-Input Multiple-Output) protocols. We have successfully validated our QG model with both TL model and laboratory measurements. The growth of Eigenvalues compares well with Weyl’s law and the level-spacing distribution agrees so well RMT predictions. The results we achieved in the MIMO application compares favourably with the prediction of a parallel on-going research (sponsored by NEMF21.)

Keywords: eigenvalues, multiple-input multiple-output, quantum graph, random matrix theory, transmission line

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Authors: Bohuslava Juhasova, Martin Juhas, Renata Masarova, Zuzana Sutova

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The article deals with the tool in Matlab GUI form that is designed to analyse a mechatronic system sensitivity and tolerance. In the analysed mechatronic system, a torque is transferred from the drive to the load through a coupling containing flexible elements. Different methods of control system design are used. The classic form of the feedback control is proposed using Naslin method, modulus optimum criterion and inverse dynamics method. The cascade form of the control is proposed based on combination of modulus optimum criterion and symmetric optimum criterion. The sensitivity is analysed on the basis of absolute and relative sensitivity of system function to the change of chosen parameter value of the mechatronic system, as well as the control subsystem. The tolerance is analysed in the form of determining the range of allowed relative changes of selected system parameters in the field of system stability. The tool allows to analyse an influence of torsion stiffness, torsion damping, inertia moments of the motor and the load and controller(s) parameters. The sensitivity and tolerance are monitored in terms of the impact of parameter change on the response in the form of system step response and system frequency-response logarithmic characteristics. The Symbolic Math Toolbox for expression of the final shape of analysed system functions was used. The sensitivity and tolerance are graphically represented as 2D graph of sensitivity or tolerance of the system function and 3D/2D static/interactive graph of step/frequency response.

Keywords: mechatronic systems, Matlab GUI, sensitivity, tolerance

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Authors: Rabiaal Adawiyah Shazali, Corina Joseph

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The disclosure of Intellectual Capital (IC) information is getting more vital in today’s era of a knowledge-based economy. Companies are advised by accounting bodies to enhance IC disclosure which complements the conventional financial disclosures. There are no accounting standards for Intellectual Capital Disclosure (ICD), therefore the disclosure is entirely voluntary. Hence, this study aims to investigate the extent of ICD and to examine the relationship between corporate governance and ICD in Malaysia. This study employed content analysis of 100 annual reports by the top 100 public listed companies in Malaysia during 2012. The uniqueness of this study lies on its underpinning theory used where it applies the institutional isomorphism theory to support the effect of the attributes of corporate governance towards ICD. In order to achieve the stated objective, multiple regression analysis were employed to conduct this study. From the descriptive statistics, it was concluded that public listed companies in Malaysia have increased their awareness towards the importance of ICD. Furthermore, results from the multiple regression analysis confirmed that corporate governance affects the company’s ICD where the frequency of audit committee meetings and the board size has positively influenced the level of ICD in companies. Findings from this study would provide an incentive for companies in Malaysia to enhance the disclosure of IC. In addition, this study would assist Bursa Malaysia and other regulatory bodies to come up with a proper guideline for the disclosure of IC.

Keywords: annual report, content analysis, corporate governance, intellectual capital disclosure

Procedia PDF Downloads 215

Authors: Ralph Adaimy, Wassim El-Hajj, Ghassen Ben Brahim, Hazem Hajj, Haidar Safa

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Huge amounts of data and personal information are being sent to and retrieved from web applications on daily basis. Every application has its own confidentiality and integrity policies. Violating these policies can have broad negative impact on the involved company’s financial status, while enforcing them is very hard even for the developers with good security background. In this paper, we propose a framework that enforces security-by-construction in web applications. Minimal developer effort is required, in a sense that the developer only needs to annotate database attributes by a security class. The web application code is then converted into an intermediary representation, called Extended Program Dependence Graph (EPDG). Using the EPDG, the provided annotations are propagated to the application code and run against generic security enforcement rules that were carefully designed to detect insecure information flows as early as they occur. As a result, any violation in the data’s confidentiality or integrity policies is reported. As a proof of concept, two PHP web applications, Hotel Reservation and Auction, were used for testing and validation. The proposed system was able to catch all the existing insecure information flows at their source. Moreover and to highlight the simplicity of the suggested approaches vs. existing approaches, two professional web developers assessed the annotation tasks needed in the presented case studies and provided a very positive feedback on the simplicity of the annotation task.

Keywords: web applications security, secure information flow, program dependence graph, database annotation

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Authors: Meng-Jou Chien, Jheng-Cheng Chen, Chang-Hsiung Tsai

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Let maxζG(m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. The n-dimensional augmented cube, denoted as AQn, a variation of the hypercube, possesses some properties superior to those of the hypercube. We study the cases when G is the augmented cube AQn.

Keywords: interconnection network, augmented cube, induced subgraph, bisection width

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Authors: Christoph Opperer

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Space syntax is a theory and method for analyzing the spatial layout of buildings and urban environments to understand how they can influence patterns of human movement, social interaction, and behavior. While direct visibility is a key factor in space syntax research, important visual information such as light, color, texture, etc., are typically not considered, even though psychological studies have shown a strong correlation to the human perceptual experience within physical space – with light and color, for example, playing a crucial role in shaping the perception of spaciousness. Furthermore, these surface properties are often the visual features that are most salient and responsible for drawing attention to certain elements within the environment. This paper explores the potential of integrating these factors into general space syntax methods and visibility-based analysis of space, particularly for architectural spatial layouts. To this end, we use a combination of geometric (isovist) and topological (visibility graph) approaches together with image-based methods, allowing a comprehensive exploration of the relationship between spatial geometry, visual aesthetics, and human experience. Custom-coded ray-tracing techniques are employed to generate spherical panorama images, encoding three-dimensional spatial data in the form of two-dimensional images. These images are then processed through computer vision algorithms to generate saliency-maps, which serve as a visual representation of areas most likely to attract human attention based on their visual properties. The maps are subsequently used to weight the vertices of isovists and the visibility graph, placing greater emphasis on areas with high saliency. Compared to traditional methods, our weighted visibility analysis introduces an additional layer of information density by assigning different weights or importance levels to various aspects within the field of view. This extends general space syntax measures to provide a more nuanced understanding of visibility patterns that better reflect the dynamics of human attention and perception. Furthermore, by drawing parallels to traditional isovist and VGA analysis, our weighted approach emphasizes a crucial distinction, which has been pointed out by Ervin and Steinitz: the difference between what is possible to see and what is likely to be seen. Therefore, this paper emphasizes the importance of including surface properties in visibility-based analysis to gain deeper insights into how people interact with their surroundings and to establish a stronger connection with human attention and perception.

Keywords: space syntax, visibility analysis, isovist, visibility graph, visual features, human perception, saliency detection, raytracing, spherical images

Procedia PDF Downloads 74

Authors: C. M. Nur Syazwani, M. K. Ahmad Imran, Rizal E. M. Nasir

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The study on BWB UV begins in UiTM since 2005 and three designs have been studied and published. The latest designs are Baseline-III and inspired by birds that have features and aerodynamics behaviour of cruising birds without flapping capability. The aircraft featuring planform and configuration are similar to the bird. Baseline-III has major flaws particularly in its low lift-to-drag ratio, stability and issues regarding limited controllability. New design known as Baseline-IV replaces straight, swept wing to delta wing and have a broader tail compares to the Baseline-III’s. The objective of the study is to investigate aerodynamics of Baseline-IV bird-inspired BWB aircraft. This will be achieved by theoretical calculation and wind tunnel experiments. The result shows that both theoretical and wind tunnel experiments of Baseline-IV graph of CL and CD versus alpha are quite similar to each other in term of pattern of graph slopes and values. Baseline-IV has higher lift coefficient values at wide range of angle of attack compares to Baseline-III. Baseline-IV also has higher maximum lift coefficient, higher maximum lift-to-drag and lower parasite drag. It has stable pitch moment versus lift slope but negative moment at zero lift for zero angle-of-attack tail setting. At high angle of attack, Baseline-IV does not have stability reversal as shown in Baseline-III. Baseline-IV is proven to have improvements over Baseline-III in terms of lift, lift-to-drag ratio and pitch moment stability at high angle-of-attack.

Keywords: blended wing-body, bird-inspired blended wing-body, aerodynamic, stability

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Authors: Ho-Won Jung, Donghun Lee, Hyung-Jin Kim

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Predictive analytics (data analysis) uses a subset of measurements (the features, predictor, or independent variable) to predict another measurement (the outcome, target, or dependent variable) on a single person or unit. It applies empirical methods in statistics, operations research, and machine learning to predict the future, or otherwise unknown events or outcome on a single or person or unit, based on patterns in data. Most analyses of metabolic syndrome are not predictive analytics but statistical explanatory studies that build a proposed model (theory building) and then validate metabolic syndrome predictors hypothesized (theory testing). A proposed theoretical model forms with causal hypotheses that specify how and why certain empirical phenomena occur. Predictive analytics and explanatory modeling have their own territories in analysis. However, predictive analytics can perform vital roles in explanatory studies, i.e., scientific activities such as theory building, theory testing, and relevance assessment. In the context, this study is to demonstrate how to use our predictive analytics to support theory building (i.e., hypothesis generation). For the purpose, this study utilized a big data predictive analytics platform TM based on a co-occurrence graph. The co-occurrence graph is depicted with nodes (e.g., items in a basket) and arcs (direct connections between two nodes), where items in a basket are fully connected. A cluster is a collection of fully connected items, where the specific group of items has co-occurred in several rows in a data set. Clusters can be ranked using importance metrics, such as node size (number of items), frequency, surprise (observed frequency vs. expected), among others. The size of a graph can be represented by the numbers of nodes and arcs. Since the size of a co-occurrence graph does not depend directly on the number of observations (transactions), huge amounts of transactions can be represented and processed efficiently. For a demonstration, a total of 13,254 metabolic syndrome training data is plugged into the analytics platform to generate rules (potential hypotheses). Each observation includes 31 predictors, for example, associated with sociodemographic, habits, and activities. Some are intentionally included to get predictive analytics insights on variable selection such as cancer examination, house type, and vaccination. The platform automatically generates plausible hypotheses (rules) without statistical modeling. Then the rules are validated with an external testing dataset including 4,090 observations. Results as a kind of inductive reasoning show potential hypotheses extracted as a set of association rules. Most statistical models generate just one estimated equation. On the other hand, a set of rules (many estimated equations from a statistical perspective) in this study may imply heterogeneity in a population (i.e., different subpopulations with unique features are aggregated). Next step of theory development, i.e., theory testing, statistically tests whether a proposed theoretical model is a plausible explanation of a phenomenon interested in. If hypotheses generated are tested statistically with several thousand observations, most of the variables will become significant as the p-values approach zero. Thus, theory validation needs statistical methods utilizing a part of observations such as bootstrap resampling with an appropriate sample size.

Keywords: explanatory modeling, metabolic syndrome, predictive analytics, theory building

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Authors: Wenjun Hou, Marek Perkowski

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The Traveling Salesman problem is famous in computing and graph theory. In short, it asks for the Hamiltonian cycle of the least total weight in a given graph with N nodes. All variations on this problem, such as those with K-bounded-degree nodes, are classified as NP-complete in classical computing. Although several papers propose theoretical high-level designs of quantum algorithms for the Traveling Salesman Problem, no quantum circuit implementation of these algorithms has been created up to our best knowledge. In contrast to previous papers, the goal of this paper is not to optimize some abstract complexity measures based on the number of oracle iterations, but to be able to evaluate the real circuit and time costs of the quantum computer. Using the emerging quantum programming language Q# developed by Microsoft, which runs quantum circuits in a quantum computer simulation, an implementation of the bounded-degree problem and its respective quantum circuit were created. To apply Grover’s algorithm to this problem, a quantum oracle was designed, evaluating the cost of a particular set of edges in the graph as well as its validity as a Hamiltonian cycle. Repeating the Grover algorithm with an oracle that finds successively lower cost each time allows to transform the decision problem to an optimization problem, finding the minimum cost of Hamiltonian cycles. N log₂ K qubits are put into an equiprobablistic superposition by applying the Hadamard gate on each qubit. Within these N log₂ K qubits, the method uses an encoding in which every node is mapped to a set of its encoded edges. The oracle consists of several blocks of circuits: a custom-written edge weight adder, node index calculator, uniqueness checker, and comparator, which were all created using only quantum Toffoli gates, including its special forms, which are Feynman and Pauli X. The oracle begins by using the edge encodings specified by the qubits to calculate each node that this path visits and adding up the edge weights along the way. Next, the oracle uses the calculated nodes from the previous step and check that all the nodes are unique. Finally, the oracle checks that the calculated cost is less than the previously-calculated cost. By performing the oracle an optimal number of times, a correct answer can be generated with very high probability. The oracle of the Grover Algorithm is modified using the recalculated minimum cost value, and this procedure is repeated until the cost cannot be further reduced. This algorithm and circuit design have been verified, using several datasets, to generate correct outputs.

Keywords: quantum computing, quantum circuit optimization, quantum algorithms, hybrid quantum algorithms, quantum programming, Grover’s algorithm, traveling salesman problem, bounded-degree TSP, minimal cost, Q# language

Procedia PDF Downloads 190

Authors: Thanusha D. Abeywickrama, Inoka C. Perera, Genji Kurisu

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Tuberculosis, considered being as the ninth leading cause of death worldwide, cause from a single infectious agent M. tuberculosis and the drug resistance nature of this bacterium is a continuing threat to the world. Therefore TB preventing treatment is expanding, where this study designed to analyze the regulatory mechanism of GntR transcriptional regulator gene Rv0792c, which lie between several genes codes for some hypothetical proteins, a monooxygenase and an oxidoreductase. The gene encoding Rv0792c was cloned into pET28a and expressed protein was purified to near homogeneity by Nickel affinity chromatography. It was previously reported that the protein binds within the intergenic region (BS region) between Rv0792c gene and monooxygenase (Rv0793). This resulted in binding of three protein molecules with the BS region suggesting tight control of monooxygenase as well as its own gene. Since monooxygenase plays a key role in metabolism, this gene may have a global regulatory role. The natural ligand for this regulator is still under investigation. In relation to the Rv0792 protein structure, a Circular Dichroism (CD) spectrum was carried out to determine its secondary structure elements. Percentage-wise, 17.4% Helix, 21.8% Antiparallel, 5.1% Parallel, 12.3% turn and 43.5% other were revealed from CD spectrum data under room temperature. Differential Scanning Calorimetry (DSC) was conducted to assess the thermal stability of Rv0792, which the melting temperature of protein is 57.2 ± 0.6 °C. The graph of heat capacity (Cp) versus temperature for the best fit was obtained for non-two-state model, which concludes the folding of Rv0792 protein occurs through stable intermediates. Peak area (∆HCal ) and Peak shape (∆HVant ) was calculated from the graph and ∆HCal / ∆HVant was close to 0.5, suggesting dimeric nature of the protein.

Keywords: CD spectrum, DSC analysis, GntR transcriptional regulator, protein structure

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Authors: M. Nekri, A. Khelladi

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The world wide web network is a network with a complex topology, the main properties of which are the distribution of degrees in power law, A low clustering coefficient and a weak average distance. Modeling the web as a graph allows locating the information in little time and consequently offering a help in the construction of the research engine. Here, we present a model based on the already existing probabilistic graphs with all the aforesaid characteristics. This work will consist in studying the web in order to know its structuring thus it will enable us to modelize it more easily and propose a possible algorithm for its exploration.

Keywords: clustering coefficient, preferential attachment, small world, web community

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Authors: P. G. Romeo

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A Lie group is a highly sophisticated structure which is a smooth manifold whose underlying set of elements is equipped with the structure of a group such that the group multiplication and inverse-assigning functions are smooth. This structure was introduced by the Norwegian mathematician So- phus Lie who founded the theory of continuous groups. The Lie groups are well developed and have wide applications in areas including Mathematical Physics. There are several advances and generalizations for Lie groups and Lie groupoids is one such which is termed as a "many-object generalization" of Lie groups. A groupoid is a category whose morphisms are all invertible, obviously, every group is a groupoid but not conversely. Definition 1. A Lie groupoid G ⇒ M is a groupoid G on a base M together with smooth structures on G and M such that the maps α, β: G → M are surjective submertions, the object inclusion map x '→ 1x, M → G is smooth, and the partial multiplication G ∗ G → G is smooth. A bundle is a triple (E, p, B) where E, B are topological spaces p: E → B is a map. Space B is called the base space and space E is called total space and map p is the projection of the bundle. For each b ∈ B, the space p−1(b) is called the fibre of the bundle over b ∈ B. Intuitively a bundle is regarded as a union of fibres p−1(b) for b ∈ B parametrized by B and ’glued together’ by the topology of the space E. A cross-section of a bundle (E, p, B) is a map s: B → E such that ps = 1B. Example 1. Given any space B, a product bundle over B with fibre F is (B × F, p, B) where p is the projection on the first factor. Definition 2. A principal bundle P (M, G, π) consists of a manifold P, a Lie group G, and a free right action of G on P denoted (u, g) '→ ug, such that the orbits of the action coincide with the fibres of the surjective submersion π : P → M, and such that M is covered by the domains of local sections σ: U → P, U ⊆ M, of π. Definition 3. A Lie group bundle, or LGB, is a smooth fibre bundle (K, q, M ) in which each fibre (Km = q−1(m), and the fibre type G, has a Lie group structure, and for which there is an atlas {ψi: Ui × G → KUi } such that each {ψi,m : G → Km}, is an isomorphism of Lie groups. A morphism of LGB from (K, q, M ) to (K′, q′, M′) is a morphism (F, f ) of fibre bundles such that each Fm: Km → K′ is a morphism of Lie groups. In this paper, we will be discussing the Lie groupoid bundles. Here it is seen that to a Lie groupoid Ω on base B there is associated a collection of principal bundles Ωx(B, Ωx), all of which are mutually isomorphic and conversely, associated to any principal bundle P (B, G, p) there is a groupoid called the Ehresmann groupoid which is easily seen to be Lie. Further, some interesting properties of the category of Lie groupoids and bundles will be explored.

Keywords: groupoid, lie group, lie groupoid, bundle

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Authors: Jeff Chak-Fu Wong, Tony Chun Yin Yip

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The transition from secondary school to university seems exciting for many first-year students but can be more challenging than expected. Enabling instructors to know students’ learning habits and styles enhances their understanding of the students’ learning backgrounds, allows teachers to provide better support for their students, and has therefore high potential to improve teaching quality and learning, especially in any mathematics-related courses. The aim of this research is to collect students’ data using online surveys, to analyze students’ factors using learning analytics and educational data mining and to discover the characteristics of the students at risk of falling behind in their studies based on students’ previous academic backgrounds and collected data. In this paper, we use correlation-based distance methods and mutual information for measuring student factor relationships. We then develop a factor network using the Minimum Spanning Tree method and consider further study for analyzing the topological properties of these networks using social network analysis tools. Under the framework of mutual information, two graph-based feature filtering methods, i.e., unsupervised and supervised infinite feature selection algorithms, are used to analyze the results for students’ data to rank and select the appropriate subsets of features and yield effective results in identifying the factors affecting students at risk of failing. This discovered knowledge may help students as well as instructors enhance educational quality by finding out possible under-performers at the beginning of the first semester and applying more special attention to them in order to help in their learning process and improve their learning outcomes.

Keywords: students' academic performance, correlation-based distance method, social network analysis, feature selection, graph-based feature filtering method

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Authors: Babak Bahri, Fatemeh Yassaee Meybodi, Changiz Eslahchi

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In the pursuit of effective cancer therapies, the exploration of combinatorial drug regimens is crucial to leverage synergistic interactions between drugs, thereby improving treatment efficacy and overcoming drug resistance. However, identifying synergistic drug pairs poses challenges due to the vast combinatorial space and limitations of experimental approaches. This study introduces ClusterSyn, a machine learning (ML)-powered framework for classifying anti-cancer drug synergy scores. ClusterSyn employs a two-step approach involving drug clustering and synergy score prediction using a fully connected deep neural network. For each cell line in the training dataset, a drug graph is constructed, with nodes representing drugs and edge weights denoting synergy scores between drug pairs. Drugs are clustered using the Markov clustering (MCL) algorithm, and vectors representing the similarity of drug pairs to each cluster are input into the deep neural network for synergy score prediction (synergy or antagonism). Clustering results demonstrate effective grouping of drugs based on synergy scores, aligning similar synergy profiles. Subsequently, neural network predictions and synergy scores of the two drugs on others within their clusters are used to predict the synergy score of the considered drug pair. This approach facilitates comparative analysis with clustering and regression-based methods, revealing the superior performance of ClusterSyn over state-of-the-art methods like DeepSynergy and DeepDDS on diverse datasets such as Oniel and Almanac. The results highlight the remarkable potential of ClusterSyn as a versatile tool for predicting anti-cancer drug synergy scores.

Keywords: drug synergy, clustering, prediction, machine learning., deep learning

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Authors: Bikis Muhammed, Sehra Sedigh Sarvestani, Ali R. Hurson, Lasanthi Gamage

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Vehicular traffic events have overly complex spatial correlations and temporal interdependencies and are also influenced by environmental events such as weather conditions. To capture these spatial and temporal interdependencies and make more realistic vehicular traffic predictions, graph neural networks (GNN) based traffic prediction models have been extensively utilized due to their capability of capturing non-Euclidean spatial correlation very effectively. However, most of the already existing GNN-based traffic prediction models have some limitations during learning complex and dynamic spatial and temporal patterns due to the following missing factors. First, most GNN-based traffic prediction models have used static distance or sometimes haversine distance mechanisms between spatially separated traffic observations to estimate spatial correlation. Secondly, most GNN-based traffic prediction models have not incorporated environmental events that have a major impact on the normal traffic states. Finally, most of the GNN-based models did not use an attention mechanism to focus on only important traffic observations. The objective of this paper is to study and make real-time vehicular traffic predictions while incorporating the effect of weather conditions. To fill the previously mentioned gaps, our prediction model uses a real-time driving distance between sensors to build a distance matrix or spatial adjacency matrix and capture spatial correlation. In addition, our prediction model considers the effect of six types of weather conditions and has an attention mechanism in both spatial and temporal data aggregation. Our prediction model efficiently captures the spatial and temporal correlation between traffic events, and it relies on the graph attention network (GAT) and Bidirectional bidirectional long short-term memory (Bi-LSTM) plus attention layers and is called GAT-BILSTMA.

Keywords: deep learning, real time prediction, GAT, Bi-LSTM, attention

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Authors: Souad Slimani, Sylvain Gravier, Simon Schmidt

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Recently, several vertex identifying notions were introduced (identifying coloring, lid-coloring,...); these notions were inspired by identifying codes. All of them, as well as original identifying code, is based on separating two vertices according to some conditions on their closed neighborhood. Therefore, twins can not be identified. So most of known results focus on twin-free graph. Here, we show how twins can modify optimal value of vertex-identifying parameters for identifying coloring and locally identifying coloring.

Keywords: identifying coloring, locally identifying coloring, twins, separating

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Authors: Yuxi Liu, Boris Belousov, Mehrzad Esmaeili Charkhab, Oliver Tessmann

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This paper presents a computational solution for designing reconfigurable interlocking structures that are fully assembled with SL Blocks. Formed by S-shaped and L-shaped tetracubes, SL Block is a specific type of interlocking puzzle. Analogous to molecular self-assembly, the aggregation of SL blocks will build a reversible hierarchical and discrete system where a single module can be numerously replicated to compose semi-interlocking components that further align, wrap, and braid around each other to form complex high-order aggregations. These aggregations can be disassembled and reassembled, responding dynamically to design inputs and changes with a unique capacity for reconfiguration. To use these aggregations as architectural structures, we developed computational tools that automate the configuration of SL blocks based on architectural design objectives. There are three critical phases in our work. First, we revisit the hierarchy of the SL block system and devise a top-down-type design strategy. From this, we propose two key questions: 1) How to translate 3D polyominoes into SL block assembly? 2) How to decompose the desired voxelized shapes into a set of 3D polyominoes with interlocking joints? These two questions can be considered the Hamiltonian path problem and the 3D polyomino tiling problem. Then, we derive our solution to each of them based on two methods. The first method is to construct the optimal closed path from an undirected graph built from the voxelized shape and translate the node sequence of the resulting path into the assembly sequence of SL blocks. The second approach describes interlocking relationships of 3D polyominoes as a joint connection graph. Lastly, we formulate the desired shapes and leverage our methods to achieve their reconfiguration within different levels. We show that our computational strategy will facilitate the efficient design of hierarchical interlocking structures with a self-replicating geometric module.

Keywords: computational design, SL-blocks, 3D polyomino puzzle, combinatorial problem

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Authors: Amirhossein Dodankeh, Hadi Dabiryan, Saeed Hamze

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Using fabrics to reinforce composites considerably leads to improved mechanical properties, including resistance to the impact load and the energy absorption of composites. Warp-knitted spacer fabrics (WKSF) are fabrics consisting of two layers of warp-knitted fabric connected by pile yarns. These connections create a space between the layers filled by pile yarns and give the fabric a three-dimensional shape. Today because of the unique properties of spacer fabrics, they are widely used in the transportation, construction, and sports industries. Polyurethane (PU) foams are commonly used as energy absorbers, but WKSF has much better properties in moisture transfer, compressive properties, and lower heat resistance than PU foam. It seems that the use of warp-knitted spacer fabric reinforced PU foam (WKSFRF) can lead to the production and use of composite, which has better properties in terms of energy absorption from the foam, its mold formation is enhanced, and its mechanical properties have been improved. In this paper, the energy absorption efficiency (EAE) of WKSFRF under low-velocity impact is investigated experimentally. The contribution of the effect of each of the structural parameters of the WKSF on the absorption of impact energy has also been investigated. For this purpose, WKSF with different structures such as two different thicknesses, small and large mesh sizes, and position of the meshes facing each other and not facing each other were produced. Then 6 types of composite samples with different structural parameters were fabricated. The physical properties of samples like weight per unit area and fiber volume fraction of composite were measured for 3 samples of any type of composites. Low-velocity impact with an initial energy of 5 J was carried out on 3 samples of any type of composite. The output of the low-velocity impact test is acceleration-time (A-T) graph with a lot deviation point, in order to achieve the appropriate results, these points were removed using the FILTFILT function of MATLAB R2018a. Using Newtonian laws of physics force-displacement (F-D) graph was drawn from an A-T graph. We know that the amount of energy absorbed is equal to the area under the F-D curve. Determination shows the maximum energy absorption is 2.858 J which is related to the samples reinforced with fabric with large mesh, high thickness, and not facing of the meshes relative to each other. An index called energy absorption efficiency was defined, which means absorption energy of any kind of our composite divided by its fiber volume fraction. With using this index, the best EAE between the samples is 21.6 that occurs in the sample with large mesh, high thickness, and meshes facing each other. Also, the EAE of this sample is 15.6% better than the average EAE of other composite samples. Generally, the energy absorption on average has been increased 21.2% by increasing the thickness, 9.5% by increasing the size of the meshes from small to big, and 47.3% by changing the position of the meshes from facing to non-facing.

Keywords: composites, energy absorption efficiency, foam, geometrical parameters, low-velocity impact, warp-knitted spacer fabric

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Authors: V. Yu. Volgutov, A. I. Orlova, S. A. Khainakov

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NaZr2(PO4)3 (NZP) and their structural analogues are characterized by a peculiar behaviors on heating – they have different expansion and contraction along different crystallographic directions due to specific arrangements of crystal structure in these compounds. An important feature of such structures is the ability to incorporate into their structural analogues wide variety of metal cations having different size and oxidation states, with different combinations and concentrations. These cations are located in different crystallographic non-equivalent positions of octahedral tetrahedral crystal framework as well as in inter-framework cavities. Through, due to iso- and hetero-valent isomorphism of the cations (and the anions) in NZP, it becomes possible to tuning the compositions and to obtain the compounds with ‘on a plan’ properties. For the design of compounds with low and ultra-low thermal expansion including those with tailored thermal expansion properties, the following crystallochemical principles it seems are promising: 1) Insertion into crystal M1 position the cations having different sizes and, 2) the variation in the composition of compounds, providing different occupation of crystal M1 position. Following these principles we have designed and synthesized the next NZP-type phosphates series: a) where radii of the cations in the M1 crystal position was varied: Zr1/4Zr2(PO4)3 - Th1/4Zr2(PO4)3 (series I); R1/3Zr2(PO4)3 where R= Nd, Eu, Er (series II), b) where the occupation of M1 crystal position was varied: Zr1/4Zr2(PO4)3-Er1/3Zr2(PO4)3 (series III) and Zr1/4Zr2(PO4)3-Sr1/2Zr2(PO4)3 (series IV). The thermal expansion parameters were determined over the range of 25-800ºC. For each series the minimum axial coefficient of thermal expansion αa = αb, αc and their anisotropy Δα = Iαa - αcI, 10-6 K-1 was found as next: -1.51, 1.07, 2.58 for Th1/4Zr2(PO4)3 (series I); -0.72, 0.10, 0.81 for Nd1/3Zr2(PO4)3 (series II); -2.78, 1.35, 4.12 for Er1/6Zr1/8Zr2(PO4)3 (series III); 2.23, 1.32, 0.91 for Sr1/2Zr2(PO4)3 (series IV). The measured tendencies of the thermal expansion of crystals were in good agreement with predicted ones. For one of the members from the studied phosphates namely Th1/16Zr3/16Zr2(PO4)3 structural refinement have been carried out at 25, 200, 600, and 800°C. The dependencies of the structural parameters with the temperature have been determined.

Keywords: high-temperature crystallography, NaZr2(PO4)3, (NZP) analogs, structural-chemical principles, tuning thermal expansion

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Authors: Fahimeh Palizban, Farshad Noravesh, Amir Hossein Saeidian, Mahya Mehrmohamadi

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In the recent decade, the emergence of liquid biopsy has significantly improved cancer monitoring and detection. Dying cells, including those originating from tumors, shed their DNA into the blood and contribute to a pool of circulating fragments called cell-free DNA. Accordingly, identifying the tissue origin of these DNA fragments from the plasma can result in more accurate and fast disease diagnosis and precise treatment protocols. Open chromatin regions are important epigenetic features of DNA that reflect cell types of origin. Profiling these features by DNase-seq, ATAC-seq, and histone ChIP-seq provides insights into tissue-specific and disease-specific regulatory mechanisms. There have been several studies in the area of cancer liquid biopsy that integrate distinct genomic and epigenomic features for early cancer detection along with tissue of origin detection. However, multimodal analysis requires several types of experiments to cover the genomic and epigenomic aspects of a single sample, which will lead to a huge amount of cost and time. To overcome these limitations, the idea of predicting OCRs from WGS is of particular importance. In this regard, we proposed a computational approach to target the prediction of open chromatin regions as an important epigenetic feature from cell-free DNA whole genome sequence data. To fulfill this objective, local sequencing depth will be fed to our proposed algorithm and the prediction of the most probable open chromatin regions from whole genome sequencing data can be carried out. Our method integrates the signal processing method with sequencing depth data and includes count normalization, Discrete Fourie Transform conversion, graph construction, graph cut optimization by linear programming, and clustering. To validate the proposed method, we compared the output of the clustering (open chromatin region+, open chromatin region-) with previously validated open chromatin regions related to human blood samples of the ATAC-DB database. The percentage of overlap between predicted open chromatin regions and the experimentally validated regions obtained by ATAC-seq in ATAC-DB is greater than 67%, which indicates meaningful prediction. As it is evident, OCRs are mostly located in the transcription start sites (TSS) of the genes. In this regard, we compared the concordance between the predicted OCRs and the human genes TSS regions obtained from refTSS and it showed proper accordance around 52.04% and ~78% with all and the housekeeping genes, respectively. Accurately detecting open chromatin regions from plasma cell-free DNA-seq data is a very challenging computational problem due to the existence of several confounding factors, such as technical and biological variations. Although this approach is in its infancy, there has already been an attempt to apply it, which leads to a tool named OCRDetector with some restrictions like the need for highly depth cfDNA WGS data, prior information about OCRs distribution, and considering multiple features. However, we implemented a graph signal clustering based on a single depth feature in an unsupervised learning manner that resulted in faster performance and decent accuracy. Overall, we tried to investigate the epigenomic pattern of a cell-free DNA sample from a new computational perspective that can be used along with other tools to investigate genetic and epigenetic aspects of a single whole genome sequencing data for efficient liquid biopsy-related analysis.

Keywords: open chromatin regions, cancer, cell-free DNA, epigenomics, graph signal processing, correlation clustering

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Authors: Shankaran Sitarama

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New Product Development (NPD) is invariably a team effort and involves effective teamwork. NPD team has members from different disciplines coming together and working through the different phases all the way from conceptual design phase till the production and product roll out. Creativity and Innovation are some of the key factors of successful NPD. Team members going through the different phases of NPD interact and work closely yet challenge each other during the design phases to brainstorm on ideas and later converge to work together. These two traits require the teams to have a divergent and a convergent thinking simultaneously. There needs to be a good balance. The team dynamics invariably result in conflicts among team members. While some amount of conflict (ideational conflict) is desirable in NPD teams to be creative as a group, relational conflicts (or discords among members) could be detrimental to teamwork. Team communication truly reflect these tensions and team dynamics. In this research, team communication (emails) between the members of the NPD teams is considered for analysis. The email communication is processed through a semantic analysis algorithm (LSA) to analyze the content of communication and a semantic similarity analysis to arrive at a social network graph that depicts the communication amongst team members based on the content of communication. The amount of communication (content and not frequency of communication) defines the interaction strength between the members. Social network adjacency matrix is thus obtained for the team. Standard social network analysis techniques based on the Adjacency Matrix (AM) and Dichotomized Adjacency Matrix (DAM) based on network density yield network graphs and network metrics like centrality. The social network graphs are then rendered for visual representation using a Metric Multi-Dimensional Scaling (MMDS) algorithm for node placements and arcs connecting the nodes (representing team members) are drawn. The distance of the nodes in the placement represents the tie-strength between the members. Stronger tie-strengths render nodes closer. Overall visual representation of the social network graph provides a clear picture of the team’s interactions. This research reveals four distinct patterns of team interaction that are clearly identifiable in the visual representation of the social network graph and have a clearly defined computational scheme. The four computational patterns of team interaction defined are Central Member Pattern (CMP), Subgroup and Aloof member Pattern (SAP), Isolate Member Pattern (IMP), and Pendant Member Pattern (PMP). Each of these patterns has a team dynamics implication in terms of the conflict level in the team. For instance, Isolate member pattern, clearly points to a near break-down in communication with the member and hence a possible high conflict level, whereas the subgroup or aloof member pattern points to a non-uniform information flow in the team and some moderate level of conflict. These pattern classifications of teams are then compared and correlated to the real level of conflict in the teams as indicated by the team members through an elaborate self-evaluation, team reflection, feedback form and results show a good correlation.

Keywords: team dynamics, team communication, team interactions, social network analysis, sna, new product development, latent semantic analysis, LSA, NPD teams

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