12 Matching Annotations
1. May 2024
2. periodicos.ufpb.br periodicos.ufpb.br
1. sentimento de pertença

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3. Apr 2023
4. en.wikipedia.org en.wikipedia.org
1. boundary conditions

how many boundary condtions are needed to confirm the solution to a partial differential equation?

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5. en.wikipedia.org en.wikipedia.org
1. Three main types of nonlinear PDEs are semilinear PDEs, quasilinear PDEs, and fully nonlinear PDEs.

Three types of nonlinear equations

2. 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.

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6. Apr 2021
7. pubmed.ncbi.nlm.nih.gov pubmed.ncbi.nlm.nih.gov
1. 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.

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8. www.psicothema.es www.psicothema.es
1. 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.

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9. www.ncbi.nlm.nih.gov www.ncbi.nlm.nih.gov
1. 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.

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10. Nov 2020
11. www.plymouth.edu www.plymouth.edu
1. phosphodiesterase

Known as PDE is an enzyme that helps break down the phosphodiester bonds.

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12. Jul 2020
13. arxiv.org arxiv.org
1. 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

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14. Apr 2019
15. iphysresearch.github.io iphysresearch.github.io
1. 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:

2. 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

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16. Nov 2018
17. iphysresearch.github.io iphysresearch.github.io
1. 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