 Apr 2023

en.wikipedia.org en.wikipedia.org

boundary conditions
how many boundary condtions are needed to confirm the solution to a partial differential equation?
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en.wikipedia.org en.wikipedia.org

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 mixedpartial 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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 Apr 2021

pubmed.ncbi.nlm.nih.gov pubmed.ncbi.nlm.nih.gov

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 LArg/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.


www.psicothema.es www.psicothema.es

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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www.ncbi.nlm.nih.gov www.ncbi.nlm.nih.gov

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 morphineinduced 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.

 Nov 2020

www.plymouth.edu www.plymouth.edu

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

 Jul 2020


Di Lauro, F., Croix, J.C., Berthouze, L., & Kiss, I. (2020). PDElimits of stochastic SIS epidemics on networks. ArXiv:2007.01043 [Physics, qBio]. http://arxiv.org/abs/2007.01043

 Apr 2019

iphysresearch.github.io iphysresearch.github.io

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
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 Nov 2018

iphysresearch.github.io iphysresearch.github.io

ForwardBackward Stochastic Neural Networks: Deep Learning of Highdimensional 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
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