Find vertices of a convex polytope, constrained by hyperplanes

I am looking for a algorithm that returns the vertices of a polytope if provided with the set of hyperplanes that confine it.

In my special case the polytope is construced by the following constrains on $ \mathbb{R}^d$

  • $ \left\| x \right\|$ = 1, $ x \in \mathbb{R}^d$
  • $ 0<a_i \leq x_i\leq b_i \leq1$ , where $ x_i$ represents the i-th component of $ x$

This always generates a convex polytope which is confined by hyperplanes, if I am not mistaken. I would like to have an algorithm that returns a set of points P that are the vertices of the polytope if provided with the set of $ a_i$ ‘s and $ b_i$ ‘s

There is a special case where there exists no $ x$ that satifies this condition. Idealy this would be picked up on.

Thank you!

How can I find the whereabouts of a specific person?

I am playing in D&D 4e campaign, and in this campaign my character is looking for a specific individual. My PC knows this individual (they were/are married) very well, and has a part of the target’s body (a lock of hair). I’d like to find this individual, using either spells (wizard or other classes), rituals, magic items, or any another technique, as long as it can be found in some D&D rulebook.

I most likely cannot track this person via mundane means, because they could be anywhere on the entire continent.

For context, my PC is level 8, but I am also willing to hear answers that apply to higher levels, so that I can plan on using them once I reach those levels.

Are there any spells, rituals, magic items, or other techniques that can be used to locate or contact a person whose whereabouts I do now know?

Why is it hard for theoretical computer scientists to find funding?

From Funding a Revolution: Government Support for Computing Research,

funding for theoretical computer science has declined as a percentage of the NSF budget for computing research (it constituted 7 percent of the budget in 1996, down from 20 percent in 1973)

I have heard quite often that theoretical computer scientists are starved for funding. I don’t see why, if the theoretical CS includes work relevant to all computing disciplines, that such research would not be prioritized. Are the implications of TCS research not clear or immediate enough to attract investment?

Find if there is matrix that satisfying the following conditions

Given a matrix $ A_{n\times n} = \{a_{ij}\}$ such that $ a_{ij}$ is a non-negative number and given 2 vectors $ (r_1,r_2,…,r_n)$ , $ (c_1,c_2,…,c_n)$ such that $ r_i,c_i\in \mathbb{Z}$ define an efficient algorithm that will determine if there’s a matrix $ B_{n\times n} = \{b_{ij}\}$ , $ b_{ij} \in \mathbb{Z}$ and

for every $ 1\leq i \leq n \sum b_{ij} = r_i$

for every $ 1\leq j \leq n \sum b_{ij} = c_j$

and

$ 0 \leq b_{ij} \leq a_{ij}$

Thought something with dynamic programming but didn’t manage to solve it.

Find how by which actions users move through my website

I have a very simple e-commerce.

As you can see in the image, people move from the product page to the checkout page and then in most cases back to the product page.

Might be that people just click on the back button, but maybe there is some other way (maybe some error?) that makes them go back to the product page. I would love to know what people do on the checkout page to go to the product page so I can think of what to do to avoid this and make the confirm their order.

Google Analytics only shows me the flow, but not the actions taken.

Is there any way or tool that can help me?

enter image description here

Where can I find errata for Psionics Unleashed/Ultimate Psionics?

I recall, at one point, there being a collection of patches to Dreamscarred Press’s psionics content, found on their forum, but it seems that in the time since I checked it, they’ve replaced their old forum with a new one.

Where can I find critical patches for my softcover copy of the original Psionics Unleashed, or my 2013 digital version of Ultimate Psionics, to give to my players and to rely on when rules conflicts come up?

The text found on external sites like d20pfsrd or the Library of Metzofitz will not do for my purposes.

I cant find a solution for a question of an array about prefix sum?

if I was given the shuffled array of a combination of prefix sum array and suffix sum array as Input. How to find out the number of initial array possible which can produce input array (combination prefix and suffix sum arrays).

How will we find whether an input array is valid as sum of prefix sum array and suffix sum array

How do I find out who wrote a note?

So I’m playing in a campaign right now, and my party has just received a threatening letter that was left in their dining room stuck to the wall with a dagger. We don’t know the writers actual name, which is what we’re trying to find out.

Currently we consist of:

  • Human Cleric 5
  • Aasimar Shaman 5
  • Elf Unchained Sumoner 5
  • Human Cavalier 5
  • Ifrit Unchained Rogue 3/AntiPaladin 2

What spells/abilities/skills can we use to determine who left it? I’ve already thought of the spell Scrying, and we were able to pick up a scroll of it at the local temple, but we weren’t able to test it out before the end of the last session, so I’m looking for backup options.

Find expectation with Chernoff bound

We have a group of employees and their company will assign a prize to as many employees as possible by finding the ones probably better than the rest. The company assigned the same $ 2$ tasks to every employee and scored their results with $ 2$ values $ x, y$ both in $ [0, 1]$ . The company selects the best employees among the others, if there is no other employee with a better score in both tasks.

Knowing that both scores are uniformly distributed in $ [0, 1]$ , how can i proof that the number of the employees receiving the price is estimated near to $ \log n$ , with $ n$ the number of the employees, having high probability?

I need to use Chernoff bound to bound the probability, that the number of winning employees is higher than $ \log n$ .