@TedShifrin it is definitely programming, I copy pasted some of the code but the issue is he doesn't provide enough context about what the problem is that he's trying to solve. I can understand it better largely because I can understand the code and even then it isn't enough for me to answer the problem
I've been wondering. How does a post make it to "hot network posts" section? I had one question that made it there, and I answered a question that also later made it there. Is it just an algorithm
technically, at a later stage, there should also be $s_i$ parallel to the $t_i$, homotopies between those , two new homotopies in place of the $H_j$ that fulfill the same purpose to the $s_i$ as the $H_j$ do to the $t_i$ and then two coherent homotopies of homotopies between those
basically, the front and back end of the diagram are fixed and the rest is something of a morphism between the front and back end and then I will consider homotopies between those (however, since the morphism itself involves homotopies, homotopies thereof will involve homotopies of homotopies)
at this point, it's been more of a struggle to try and figure out non-awful notation than it has been to prove the result I'm trying to write down
I do make an attempt at streamlining, lowercase letters are continuous maps, upper case letters are homotopies (and the spaces involved, but the difference between those should be clear) and homotopies of homotopies will be greek letters
@D.C.theIII you should get $Q(\beta+h)-Q(\beta) - 2 (X \beta -Y)^T Xh = h^T X^T X h$, and since the term on the rhs is $O(\|h\|^2)$ it is differentiable with $DQ(\beta)h = 2 (X \beta -Y)^T Xh$. If one must use the gradient, it is just $\nabla Q(\beta) = X^T(X \beta -Y)$.
I do like to write $H_t=H(-,t)$ for homotopies (and similarly for the homotopies of homotopies), but sadly that conflicts with calling the homotopies in the picture $H_1$ and $H_2$, which is why I need to change something
if I have a markov chain $(X_n)_n$ with values in $S$ with transition matrix $Q$ and initial distribution $\nu$ what can I say about $E_\nu(Q(X_{n+1},y)|F_n)$ for all $y\in S$?
I am thinking about using the simple markov property but I don't see how
If we had pizza together you'd see me sitting at a completely separate table away from everyone else, as I do with my own family too. I'm not just good at "eating together"
Hi everyone! I started a 2nd attempt at a PhD a couple of months ago. The 1st was downgraded to an MPhil due to health & financial issues. I'm concerned the same thing might happen again. I'm studying linear algebraic groups and, so far, I'm learning a lot of algebraic geometry; it's tough. I started strong but old habits, like sleeping in until late, are returning.
I have an assignment due by the end of the month. It's causing stress. I asked for an extension on Friday.
I'm not sure what I'm looking for in the chat here. I guess I just need to vent.
My passion for mathematics is intense and I want to do myself justice in my studies.
@Shaun Exercise helps. During the last two quarters of my PhD (during which time my father was diagnosed with lung cancer, my father died, I was in the middle of a messy and acrimonious divorce after 12 years of marriage, oh, and a global pandemic was kicking off), I walked to campus every day (2.5 miles, each way). It helped. A lot.
I have copies of the three "Linear Algebraic Groups" textbooks - yes, they each have that title - and they each start out with a terse treatment of algebraic geometry. I asked my supervisor for guidance. He gave me a selection of exercises from one of them. I've been working on them for the last month.
@XanderHenderson I'm sorry to hear that. Thank you for the advice.
I used to exercise a lot during my undergraduate days: I hit the gym twice a week and exercised before bed each night that wasn't a gym night. Ironically, I had a long stay in hospital (for my mental health) - September 2015 to March 2017 - and I gained weight then. I got out of the habit of exercising and eating healthily.
My family are very supportive. They encourage me to lose weight a lot, almost too much really. My current university is associated with a large gym just off campus. I have a discounted membership I haven't used yet. The main barrier is having to wash my gym kit. The local laundrette has exorbitant prices.
My diagnosis is paranoid schizophrenia. It can render me inactive for a couple of days at a time. Whenever I take the time off from my studies, I feel guilty.
And then there's my budget. My 1st PhD attempt wavered my tuition fees and gave me a stipend. This attempt, however, I'm funding for myself using one of those government doctoral loans they have here in the UK.
At least here at Aberdeen, my interests are much more in line with the research I do. The previous attempt always felt like a compromise, not for lack of interest in the area.
