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I'm working on numerical methods for solving differential equations and running the JuliaDiffEq organization to build all of the newest methods into Differentia

I'm working on numerical methods for solving differential equations and running the JuliaDiffEq organization to build all of the newest methods into DifferentialEquations.jl. So much of this field is undocumented or has never been tested, so it's awesome to just come up with new ideas and new schemes and test them out. My PhD was in control of stochasticity in biological organisms (how do you control the internal randomness of biochemical reactions?) and the methods for simulating such models. So I get to work with hot off the press new biological "big data" and develop new techniques which use some of the newest advances in mathematics (stochastic analysis) to do something that can have some very practical outcomes. If you're really looking for interesting technical problems, I highly recommend looking into systems biology. There's interesting mathematical, computational, and biological problems being worked on here (with lots of funding!).

dragon96 8y ago
If you don't mind sharing, what are some of the problems in systems biology that you find more interesting, and who is working on them?
- ChrisRackauckas 8y ago
  I find the Irvine school of systems biology to be a very intriguing methodology/outlook which is based around complex models to understand unintuitive biological behaviors matched with data validation (a lot of mathematical biology is very disconnected from biology, and a lot of systems biology is more bioinformatics). For accessibility, here's some videos which will never go behind a paywall. I think Arthur Lander gives the most accessible talks. A lot of his talks around growth control [1] and pattern formation [2] where he shows the tradeoffs between different cellular network and feedback mechanisms and how this influences the robustness of development. Then you have people like me [3] and my PhD adviser Qing Nie [4] where we describe how noise, the randomness that exists in biochemical interactions, is able to be controlled and used by biological organisms to improve developmental processes. And then there's people like John Lowengrub who talk about the morphology of tumors [5] to be able to predict and describe how the behavior can be derived from the shape. There's a lot of movement going on in the data generation side of systems biology. Single-cell RNA-seq methods allow us to quantify almost all of the RNA generated by each individual cell for a whole group of cells, which lets us know exactly how cells are generating different proteins and by what amounts [6]. This of course opens up a whole lot of questions, along the big data computing side (how do you handle such a large dataset and extract something new out of?) and from the mathematical side (what kind of models is this actually validating and invalidating?). With this kind of data, there are questions about how well we can fit computational models directly to data and improve prediction accuracy beyond qualitative results [7]. These models are becoming precise enough that people are starting to test their uses in pharmocology, doing personalized drug-dosage prediction using covariates and large internal systems biological models called PBPK models [8]. [1]: https://www.youtube.com/watch?v=Dza0hM2vBNk https://www.youtube.com/watch?v=Dza0hM2vBNk [2]: https://www.youtube.com/watch?v=8jFx9I7lBOg https://www.youtube.com/watch?v=8jFx9I7lBOg [3]: https://www.youtube.com/watch?v=_h5fVDvGp-8 https://www.youtube.com/watch?v=_h5fVDvGp-8 [4]: https://www.youtube.com/watch?v=tRzrBvGqOOE https://www.youtube.com/watch?v=tRzrBvGqOOE [5]: https://www.youtube.com/watch?v=NVFFoGfC4Uk https://www.youtube.com/watch?v=NVFFoGfC4Uk [6]: https://www.youtube.com/watch?v=8KpIDpPEGV4 https://www.youtube.com/watch?v=8KpIDpPEGV4 [7]: https://www.youtube.com/watch?v=5nIeYVe_yDo https://www.youtube.com/watch?v=5nIeYVe_yDo [8]: https://www.youtube.com/watch?v=2Ut-Utim-wU https://www.youtube.com/watch?v=2Ut-Utim-wU

dragon96 8y ago

If you don't mind sharing, what are some of the problems in systems biology that you find more interesting, and who is working on them?

ChrisRackauckas 8y ago
I find the Irvine school of systems biology to be a very intriguing methodology/outlook which is based around complex models to understand unintuitive biological behaviors matched with data validation (a lot of mathematical biology is very disconnected from biology, and a lot of systems biology is more bioinformatics). For accessibility, here's some videos which will never go behind a paywall. I think Arthur Lander gives the most accessible talks. A lot of his talks around growth control [1] and pattern formation [2] where he shows the tradeoffs between different cellular network and feedback mechanisms and how this influences the robustness of development. Then you have people like me [3] and my PhD adviser Qing Nie [4] where we describe how noise, the randomness that exists in biochemical interactions, is able to be controlled and used by biological organisms to improve developmental processes. And then there's people like John Lowengrub who talk about the morphology of tumors [5] to be able to predict and describe how the behavior can be derived from the shape. There's a lot of movement going on in the data generation side of systems biology. Single-cell RNA-seq methods allow us to quantify almost all of the RNA generated by each individual cell for a whole group of cells, which lets us know exactly how cells are generating different proteins and by what amounts [6]. This of course opens up a whole lot of questions, along the big data computing side (how do you handle such a large dataset and extract something new out of?) and from the mathematical side (what kind of models is this actually validating and invalidating?). With this kind of data, there are questions about how well we can fit computational models directly to data and improve prediction accuracy beyond qualitative results [7]. These models are becoming precise enough that people are starting to test their uses in pharmocology, doing personalized drug-dosage prediction using covariates and large internal systems biological models called PBPK models [8]. [1]: https://www.youtube.com/watch?v=Dza0hM2vBNk https://www.youtube.com/watch?v=Dza0hM2vBNk [2]: https://www.youtube.com/watch?v=8jFx9I7lBOg https://www.youtube.com/watch?v=8jFx9I7lBOg [3]: https://www.youtube.com/watch?v=_h5fVDvGp-8 https://www.youtube.com/watch?v=_h5fVDvGp-8 [4]: https://www.youtube.com/watch?v=tRzrBvGqOOE https://www.youtube.com/watch?v=tRzrBvGqOOE [5]: https://www.youtube.com/watch?v=NVFFoGfC4Uk https://www.youtube.com/watch?v=NVFFoGfC4Uk [6]: https://www.youtube.com/watch?v=8KpIDpPEGV4 https://www.youtube.com/watch?v=8KpIDpPEGV4 [7]: https://www.youtube.com/watch?v=5nIeYVe_yDo https://www.youtube.com/watch?v=5nIeYVe_yDo [8]: https://www.youtube.com/watch?v=2Ut-Utim-wU https://www.youtube.com/watch?v=2Ut-Utim-wU