The descent tag has no wiki summary.
5
votes
2answers
90 views
combinatorial descents finding the number of permutations with criteria
I need help with the following:
Define a descent of a permutation to be $j$ when $p_{j+1} < p_j$. Then the descent set of a permutation is the set of all descents. For example, the ...
0
votes
0answers
47 views
Finding descent direction of quadratic function
I have a quadratic function: $f(x) = 24x_1+14x_2+x_1x_2$
and point $x_0 = (2,10)^T$ with $f(x_0) = 208$
And the first question is "give descent direction r in $x_0$"
The second question "is f convex ...
1
vote
0answers
31 views
Rate of convergence of a single-neuron Perceptron network
I'm implementing a Perceptron network which basically consists of a single neuron in a single layer, trying to learn an OR logic port (linearly separable), but using the sigmoid function as ...
3
votes
0answers
171 views
Solving Linearly Constrained Quadratic Programming with Coordinate Descent
Does anybody have any idea about how to solve the following problem with Coordinate Descent?
\begin{align}
\min &\quad \mathbf{x}^{\top}P\mathbf{x} + b^{\top}\mathbf{x}\\
\text{Subject to}& ...
1
vote
1answer
85 views
Fréchet mean between points in $\mathbb{R}^3$
Let $X$ be a set of $n$ points in $\mathbb{R}^3$ and $f_m$ be the Fréchet mean, i.e.:
$$
f_m= \arg \min_{p \in M} \sum_{i=1}^n w_id^2(p,x_i)
$$
where $(\mathbb{R}^3,d)$ is a complete metric space, ...
1
vote
0answers
56 views
Can Fermats descent be interpreted on a conic?
Fermat proved the Diophantine equation $$(x^2)^2 + (y^2)^2 = z^2$$ has only solutions $(0,0,0)$, $(0,\pm 1,\pm 1)$ and $(\pm 1,0,\pm 1)$ using "infinite descent".
The conic $C : X^2 + Y^2 - 1$ has a ...
10
votes
1answer
250 views
How to get Fermat descent working on other conics?
Fermat solved the Diophantine equation $(x^2)^2 + (y^2)^2 = z^2$ using descent, the key step was using the Pythagorean triples:
$x^2 = u^2 - v^2$
$y^2 = 2 u v$
$z = u^2 + v^2$
but then it is seen ...
1
vote
1answer
361 views
How to prove the Energy function of a Hopfield net is monotonically decreasing?
How to prove the Energy function of a Hopfield net is monotonically decreasing?
$E = -1/2 \sum_{i,j} {w_{ij}}{s_i}{s_j} + \sum_{i}^{}s_{i} \theta_i$
I'll assume a proof involves the standard ...
5
votes
0answers
178 views
Do cokernels in RingSpc automatically lead to descent?
I'm currently interested in the following result:
Let $f: X \to Y$ be a fpqc morphism of schemes. Then there is an equivalence of categories between quasi-coherent sheaves on $Y$ and "descent data" ...
