Browsing by Subject "graph theory"

Now showing 1 - 4 of 4
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    Computation of conductive thermal distribution using non-homogenous graph theory for real-time applications in metal PBF process
    (Elsevier, 2022-09) Malekipour, Ehsan; El-Mounayri, Hazim; Mechanical and Energy Engineering, Purdue School of Engineering and Technology
    The Powder Bed Fusion (PBF) process is inherently a thermal process with complex thermal interactions between different printed zones as well as different layers. There exist only a few methods such as finite element analysis (FEA), finite element differences (FDM), graph theory (GT), Goldak’s FEA, and Rosenthal equation, which are able to predict thermal temperature distribution throughout a printed layer (2D) or part (3D). All these approaches suffer from inherent limitations including the applied boundary conditions and computational time. A rapid and reliable method to compute thermal distribution throughout a printed part is pivotal to supporting real-time closed-loop monitoring and control, enabling thermal simulation software with rapid and precise prediction, and advancing current research on thermal-related abnormalities such as residual stress and distortion. The literature shows that the conventional graph theory is the fastest approach that generates relatively precise results in a fraction of the computational time of other techniques; however, the lack of a solution to the non-homogeneous governing thermal equation through GT has hampered this method in terms of thermal load resolution, accuracy in highly rapid process such as PBF, and scope of application. In this paper, we describe the characteristics that make GT a superior approach for real-time computation of thermal field compared to other similar approaches such as FDM. Also, we develop a solution to the non-homogeneous term of the thermal conduction equation by using GT. This solution represents a breakthrough for the development of precise real-time closed-loop monitoring and control systems by providing a precise numerical solution to the thermal conduction equation in a fraction of time compared with previous traditional methods such as FEA and FDM. Ongoing work includes the development of an intelligent monitoring and control system that leverages this solution in order to optimize scan strategy real-time in metal PBF.
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    Consistency of Graph Theoretical Measurements of Alzheimer’s Disease Fiber Density Connectomes Across Multiple Parcellation Scales
    (IEEE, 2022-12) Xu, Frederick; Garai, Sumita; Duong-Tran, Duy; Saykin, Andrew J.; Zha, Yize; Shen, Li; Radiology and Imaging Sciences, School of Medicine
    Graph theoretical measures have frequently been used to study disrupted connectivity in Alzheimer’s disease human brain connectomes. However, prior studies have noted that differences in graph creation methods are confounding factors that may alter the topological observations found in these measures. In this study, we conduct a novel investigation regarding the effect of parcellation scale on graph theoretical measures computed for fiber density networks derived from diffusion tensor imaging. We computed 4 network-wide graph theoretical measures of average clustering coefficient, transitivity, characteristic path length, and global efficiency, and we tested whether these measures are able to consistently identify group differences among healthy control (HC), mild cognitive impairment (MCI), and AD groups in the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort across 5 scales of the Lausanne parcellation. We found that the segregative measure of transtivity offered the greatest consistency across scales in distinguishing between healthy and diseased groups, while the other measures were impacted by the selection of scale to varying degrees. Global efficiency was the second most consistent measure that we tested, where the measure could distinguish between HC and MCI in all 5 scales and between HC and AD in 3 out of 5 scales. Characteristic path length was highly sensitive to the variation in scale, corroborating previous findings, and could not identify group differences in many of the scales. Average clustering coefficient was also greatly impacted by scale, as it consistently failed to identify group differences in the higher resolution parcellations. From these results, we conclude that many graph theoretical measures are sensitive to the selection of parcellation scale, and further development in methodology is needed to offer a more robust characterization of AD’s relationship with disrupted connectivity.
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    Marginalized Latent Semantic Encoder for Zero-Shot Learning
    (IEEE, 2019-06) Ding, Zhengming; Liu, Hongfu; Computer Information and Graphics Technology, School of Engineering and Technology
    Zero-shot learning has been well explored to precisely identify new unobserved classes through a visual-semantic function obtained from the existing objects. However, there exist two challenging obstacles: one is that the human-annotated semantics are insufficient to fully describe the visual samples; the other is the domain shift across existing and new classes. In this paper, we attempt to exploit the intrinsic relationship in the semantic manifold when given semantics are not enough to describe the visual objects, and enhance the generalization ability of the visual-semantic function with marginalized strategy. Specifically, we design a Marginalized Latent Semantic Encoder (MLSE), which is learned on the augmented seen visual features and the latent semantic representation. Meanwhile, latent semantics are discovered under an adaptive graph reconstruction scheme based on the provided semantics. Consequently, our proposed algorithm could enrich visual characteristics from seen classes, and well generalize to unobserved classes. Experimental results on zero-shot benchmarks demonstrate that the proposed model delivers superior performance over the state-of-the-art zero-shot learning approaches.
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    Preserving Graph Utility in Anonymized Social Networks? A Study on the Persistent Homology
    (IEEE, 2017-10) Gao, Tianchong; Li, Feng; Engineering Technology, School of Engineering and Technology
    Following the trend of privacy preserving online social network publishing, various anonymization mechanisms have been designed and employed. Many differential privacy-based mechanisms claim that they can preserve the utility as well as guarantee the privacy. Their utility analysis are always based on some specifically chosen metrics.This paper aims to find a novel angle that describing the network in multiple scales. Persistent homology is such a high level metric that it reveals the parameterized topological features with various scales and it is applicable for read-world applications. In this paper, four differential privacy mechanisms employing different models are analyzed under the traditional graph metrics and the persistent homology. The evaluation results demonstrate that all algorithms can partially or conditionally preserve certain traditional graph utilities, but none of them are suitable for all metrics. Furthermore, none of the existing mechanisms can fully preserve the persistent homology, especially in high dimensions, which implies that the true graph utility is lost.