Abstract In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the...
for all , where the total differential is the matrix with entries for and , where are the components of . (If one wishes, one can also view as a linear transformation from the tangent space of Lagrangian space at to the tangent space of Eulerian space at .) Equivalently, is orientation ...
Explain what is a saddle point in mathematics. Define the linear transformation T:\mathbb{C}^3\to \mathbb{C}^2,T \begin{pmatrix} \begin{bmatrix} What is homeomorphism invariant? What is the transverse axis of the hyperbola \frac{(x + 13)^{2{16} - \frac{(y - 15)^{2{4} ...
The image of Fudō Myō-ō, “Unmovable Wisdom King,” the main deity of the temple, is historically significant in that Kobo Daishi (or Kukai, the founder of Shingon Buddhism) is said to have carved, consecrated and conducted a Goma ritual before this very statue in 810, by order of ...
point in space: The quantum vacuum is a seething ocean of activity. As a result, the energy content of empty space—the vacuum energy density—and the lowest energy a quantum field can have—the zero-point energy—are both larger than zero. However, there turned out to be an ...
I know that the question is subtle, but the problem I'm having it's incredibly strange. I'm asking if MKL in its internal algorithm has a particular way to read the matrix (maybe it relies also on the size of the arrays allocated?). I know it's strange, but I have two m...
is a point of local maximum value. c) If rt−s2(a, b)<0, then (a, b) is a saddle point. d) If rt−s2(a, b)=0, then we need further investigation. We can check the conditions on a parameter c included ...
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Because |J(0.5,N0.5)|<0, (0.5,N0.5) is saddle point and therefore unstable. Similarly, we can show that (1,N1) is not a stable steady state when 0<θ(Np)<0.25. Using the same approach, we can prove (0.5,N0.5) is the unique stable steady state when θ(Np)≤0.25 and (1,N1...
What happens if the gradient is zero? If the gradient is zero, it indicates a local maximum, minimum, or saddle point, where there is no slope or direction of increase. 6 Is the Jacobian always square? No, the Jacobian matrix can be rectangular because it depends on the dimensions of th...