Recent content by nigels

I’m currently evaluating the "realism" of two survival models in R by comparing the respective Kullback-Leibler divergence between their simulated survival time dataset (`dat.s1` and `dat.s2`) and a “true”, observed survival time dataset (`dat.obs`). Initially, directed KLD functions show that...

@Chestermiller Thanks for the new knowledge! The phenomenon makes more sense to me now. :)

@SergioPL Thank you for the detailed explanation! I find your response to (3) especially useful where you described the upward force due to adjacent stress. As you mentioned, this cancels out the downward force exerted by the basketball, which I infer to mean "no bending" as long as the...

@Chestermiller Hm.. no idea..

Very dumb classic mechanics question here: The other day I caught sight of a trivial objects arrangement: a basketball placed on top of a 6-sided cardboard box on the floor, and I wondered how the weight of the hollowed sphere could cause bending on the supported, flat top surface of the box...

@Svein: Sorry, x1 and x2 mean x_1 and x_2.

In a trivial optimization problem, when seeking the value of x2 that minimizes y(x2)/(x2-x1), the solution is graphically given by the tangent line shown in the figure. I'm having a lot of difficulty understanding why this is true, i.e., the logical steps behind the equivalence supporting the...

Hi Stephen, My question does pertain to a real-world problem, and the two dependent variables are actually steady-state solutions to a set of Fokker-Planck equations modeling an advection-diffusion process given static point-attractors. So the system is spatio-temporally continuous (time...

Hi all, I'm interested in obtaining some measure of contact (or encounter) likelihood between two individuals, each is spatially distributed with some probability density function at time ##t## such that, Space use of individual 1 = ##u(\mathbf{x}, t)## Space use of individual 2 =...

I've been getting pretty rusty in terms of derivation in recent years. Encountered this problem which I can't derive the steps despite knowing the solution. \frac{\partial^2 u}{\partial r^2} + \frac{\partial u}{\partial r}\left(\beta + \frac{1}{r}\right)+\frac{\beta}{r}u=0 Known...

In a problem that requires converting from cartesian to polar coordinates, I need to take \frac{dr}{dx}. I tried doing it two different ways but getting two completely different answers.. Method 1: r=\sqrt{x^2+y^2} \frac{dr}{dx}=\frac{1}{2}\frac{1}{\sqrt{x^2+y^2}}2x \;\; =...

e^(-i * x) not well-defined. Why?? Hi, Just saw this as a step in an example that demonstrates the differentiability of holomorphic function. But I can't for the life of me figure out why e^(-2iθ) is ill-defined.

Hi group, In order to understand the methods of characteristics, I've been reading its wiki entry plus other sources. However, one of the first step of finding the normal surface vector given the PDE remains baffling to me in terms of how it's derived. In short, when provided with a(x...

θ(t) and φ(t) are just functions that modifies the diffusion coefficient K to be time-dependent. γ is defined as the "rate at which territory sizes tend to return to the mean size", which I understand as "the rate at which L_1 returns to its initial state". Yet still, I can't explain...

Thanks, tiny-tim! That makes much more sense now. However, I noticed that in the attachment, the spring constant is 1/4. Is that because the point is attached by a separate spring on both sides? Somehow that's equivalent to have two parallel springs for some reason? By the way, the paper...