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Related Concept Videos

Self-Discrepancy Theory02:45

Self-Discrepancy Theory

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One influential perspective on what motivates people's behavior is detailed in Tory Higgin's self-discrepancy theory (Higgins, 1987). He proposed that people hold disagreeing internal representations of themselves that lead to different emotional states.  
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Self-Discrepancy and Its Effects01:29

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Self-discrepancy theory explains how people compare their actual self to their ideal and ought selves and how mismatches between these self-guides can lead to emotional distress. Developed by E. Tory Higgins, the theory distinguishes among three components of self-concept: the actual self, the ideal self, and the ought self. These refer respectively to how individuals perceive themselves, how they aspire to be, and how they believe they are obligated to be. Emotional well-being, self-esteem,...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
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G-protein coupled receptors are ligand binding receptors that indirectly affect changes in the cell. The actual receptor is a single polypeptide that transverses the cell membrane seven times creating intracellular and extracellular loops. The extracellular loops create a ligand specific pocket which binds to neurotransmitters or hormones. The intracellular loops holds onto the G-protein.
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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Coupled regularization with multiple data discrepancies.

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    This study introduces coupled regularization for inverse problems, enhancing data reconstruction from multiple sources. Optimized parameter choices improve convergence rates for multi-spectral and dynamic imaging applications.

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    Area of Science:

    • Computational imaging
    • Applied mathematics
    • Medical physics

    Background:

    • Inverse problems require robust reconstruction of underlying data from indirect measurements.
    • Multi-source data (e.g., multi-spectral, multi-modality, dynamic) present unique reconstruction challenges.
    • Existing methods may not fully leverage the correlations within multi-source data.

    Purpose of the Study:

    • To develop and analyze coupled regularization methods for simultaneous data reconstruction from multiple sources.
    • To derive stability, convergence, and convergence rate guarantees for these methods.
    • To demonstrate improved performance through data-channel-specific parameter selection strategies.

    Main Methods:

    • General framework for coupled regularization in inverse problems.
    • Derivation of analytical stability and convergence results.
    • Inclusion of Kullback-Leibler divergence as a data discrepancy term.
    • Development of an algorithmic framework and source code for practical implementation.

    Main Results:

    • Theoretical guarantees for stability and convergence are established.
    • Parameter choice strategies tailored to data channel interplay enhance convergence rates.
    • The framework accommodates general data discrepancy terms, including Kullback-Leibler divergence.
    • Numerical validation is provided for multi-contrast MRI and joint MR-PET reconstruction.

    Conclusions:

    • Coupled regularization offers a powerful approach for multi-source inverse problems.
    • Adaptive parameter selection significantly boosts reconstruction efficiency and accuracy.
    • The provided framework and code facilitate the application of these advanced methods.
    • The approach shows promise for enhancing medical imaging modalities like MRI and PET.