We split the residual of the space–time reconstruction into hyperbolic and parabolic contributions and treat them in different norms.
将残差分裂为「双曲部分」和「抛物部分」并用不同范数处理——这个技巧看似平凡，实则是整篇论文最关键的工程决策。若不分裂，估计器会包含 ε⁻¹ 量级的项，在对流主导时完全失效。这类「范数分裂」策略在偏微分方程分析中是一种深刻的技巧：问题的物理本质（双曲 vs 抛物）决定了应该在哪个函数空间中度量误差。
sentimento de pertença
O metaverso nas escolas e nas universidades, também deve ser visto como um recurso pedagógico digital de apoio para portadores de necessidades especiais (PDE), porque aumenta o sentimento de pertença com a criação de avatares que podem ser programados para usar linguagem de sinais e legendas permitindo que alunos surdos ou com deficiência auditiva participem das atividades com facilidade e efetividade. Muitos alunos PDE, desistem da escola ou das universidades, porque não se sentem realmente incluídos no ambiente e muitas vezes não recebe um suporte pedagógico adequado para a inclusão e permanência na instituição. O metaverso e outros recursos inovadores aplicados aos ambientes virtuais de aprendizagem podem transformar as vidas destes jovens, tornado suas expectativas para um futuro profissional concretizáveis.
boundary conditions
how many boundary condtions are needed to confirm the solution to a partial differential equation?
Three main types of nonlinear PDEs are semilinear PDEs, quasilinear PDEs, and fully nonlinear PDEs.
Three types of nonlinear equations
A PDE is called linear if it is linear in the unknown and its derivatives
where ai and f are functions of the independent variables x and y only. (Often the mixed-partial derivatives uxy and uyx will be equated, but this is not required for the discussion of linearity.) If the ai are constants (independent of x and y) then the PDE is called linear with constant coefficients. If f is zero everywhere then the linear PDE is homogeneous, otherwise it is inhomogeneous.
Conclusion: Our data suggest that the combination of VLF with morphine may be a relevant therapeutic implication to manage pain even when tolerance to morphine exists. Moreover, our data demonstrates the involvement of L-Arg/NO/cGMP pathway in the prevention of morphine tolerance and dependence by venlafaxine.
It's not clear if this has relevance to the subjective effects. I'm starting to think that I won't get an answer anytime soon.
Results: The administration of sildenafi l reduced all of the morphine withdrawal symptoms.
An acute effect. Interesting but not particularly consequential. It does mean, however, that I need to be wary of studies using withdrawal as a netric when combining PDE5 inhibitors with opioids.
These results suggest that the elevation of the cyclic AMP levels is involved in the development of morphine withdrawal syndrome and that blockade of the morphine-induced reduction of cyclic AMP levels by chronic rolipram inhibits the development of dependence and the behavioural and biochemical changes induced by naloxone. Furthermore, rolipram may be a useful drug for attenuating the development of morphine dependence.
Excellent. This implies that theobromine may help prevent opioid tolerance.
phosphodiesterase
Known as PDE is an enzyme that helps break down the phosphodiester bonds.
Di Lauro, F., Croix, J.-C., Berthouze, L., & Kiss, I. (2020). PDE-limits of stochastic SIS epidemics on networks. ArXiv:2007.01043 [Physics, q-Bio]. http://arxiv.org/abs/2007.01043
A Discussion on Solving Partial Differential Equations using Neural Networks
有不少 insight 的讨论，如 Benefits and drawbacks of solving partial differential equations with neural networks:
Augmented Neural ODEs
神经常微分方程无法表示某些简单函数，本文提出更具表现力的增强神经ODE，可有效降低计算成本、改善泛化性
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations
惊艳到了~~ 又一篇关于求解偏微分方程的~ 拿来好好读读
Paper Summary