We propose an inexact low-rank source iteration with diffusion synthetic acceleration (SI–DSA) for solving the multidimensional steady-state radiative transfer equation (RTE) in the second-order formulation. The even parity is represented in either a low-rank matrix or hierarchical Tucker tensor (HTT) format, enabling substantial reductions in computational resources. Each SI step is solved using a preconditioned low-rank conjugate gradient (CG) method with a diffusion preconditioner. To further improve efficiency, we introduce an adaptive inexact strategy that dynamically relaxes the inner CG tolerance during early SI iterations. The method exploits the tensor-product structure of the discretized operators to perform all matrix–vector operations in low-rank form. Numerical experiments on 2D2V benchmark problems—including diffusion-dominated, transport-dominated, and multiscale problems—demonstrate that the proposed approach achieves errors on the order of 10−4−−10−5 relative to full-rank reference solutions, while reducing the degrees of freedom by up to two orders of magnitude. In the diffusion-dominated case, the low-rank solver achieves speedups exceeding 90 × over its full-rank counterpart and remains competitive in solving challenging transport-dominated and multiscale problems while providing substantial storage savings. To our knowledge, this work provides the first low-rank SI–DSA framework for multidimensional steady-state RTE.
A new mathematical model governing the development of a corrupted hierarchy is derived. This model is based on the Mean Field Games theory. A retrospective problem for that model is considered. From the applied standpoint, this problem amounts to figuring out the past activity of the corrupted hierarchy using the present data for this community. Three new Carleman estimates are derived. These estimates lead to Hölder stability estimates and uniqueness results for both that retrospective problem and its generalized version. Hölder stability estimates characterize the dependence of the error in the solution of the retrospective problem from the error in the input data.
Social media influencers play a critical role in building emotional connections between followers and brands, however evolving digital trends have reshaped what audiences value in online personalities. Grounded in persuasion theory, this study examines the characteristics of travel influencers that inspire followers’ decision-making process and enhance perceived value. A sample of 510 was collected from adults residing in the United States. Using PLS-SEM, the results showed that relatability and coolness simultaneously stimulate inspiration and strengthen emotional attachment, thereby shaping travel planning and visit intentions. Relatability exerts the strongest influence on emotional connection, while self-disclosure also positively affects attachment. Moderation analysis revealed that trust strengthens only the relationship between self-disclosure and emotional attachment; specifically, that self-disclosure is more influential when trust is low but less impactful once trust is established. Theoretically, the findings refined influencer models by positioning trust as an outcome of affective persuasion. Practically, the results can guide destinations in leveraging relatable, cool, and authentic influencers to engage audiences effectively.
Purpose Nerve transections often require surgical intervention with a bridging material to achieve meaningful recovery (MR). We explored similar cohorts with nerve reconstruction using nerve autograft or nerve allograft. We hypothesized that motor recovery in mixed and motor nerve injuries repaired with nerve allograft is noninferior to repairs with nerve autograft. Methods Subjects had mixed or motor nerve transections in the upper extremity distal to the axilla surgically repaired with nerve autograft or nerve allograft. Motor recovery outcomes were analyzed using the British Medical Research Council Classification (MRCC) with MR defined as ≥M3 and enhanced MR defined as ≥M4. Results There were 24 subjects with 25 repairs in the autograft group and 23 subjects with 25 repairs in the allograft group. Motor recovery of ≥M3 was achieved in 64% and ≥M4 in 28% of autograft repairs. In contrast, motor recovery of ≥M3 was achieved in 80.0% and ≥M4 in 60% of allograft repairs. The median (interquartile range) MRCC score in the autograft cohort was 3.0 (1.0–4.0; 95% CI, 2.0–3.0) and 4.0 (3.0–4.0; 95% CI, 3.0–4.0) in the allograft cohort. The mean (SD) MRCC score in the autograft cohort was 2.5 (1.5; 95% CI, 1.9–3.1) and 3.2 (1.4, 95% CI, 2.7–3.8) in the allograft cohort. Analysis found that return of motor function in nerve allograft was as favorable as autograft. Conclusions These findings support allograft as a reasonable alternative to autograft for upper extremity mixed and motor nerve transection injuries. Allograft performed as favorable as autograft while avoiding the need for autograft harvest and the potential donor site morbidity. Type of study/level of evidence Therapeutic III.
