# Questions tagged [simplex]

For questions on the $n$-simplex, an $n$-dimensional polytope with $n+1$ points.

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### Simplicial complex [closed]

I started to learn about "simplicial complex" and read about applications but it was very difficult for me to understand these applications, my question is as below what is the importance ...
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### The norm in the n-simplex

İ have this question and my attempt to solve it as the following : Consider an n-simplex $[p_0, p_1,...,p_n]$. If $a,b \in [p_0, > p_1,...,p_n]$, then show that $||a − b|| \leq \sup_i ||a − p_i||$....
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### Simplex : minimum of objective function is zero when ..

I run simplex (hopefully right) with break ties rules and everything for a minimisation problem. If I end up with the same base made of variables that are not in the cost function and there's no ...
1 vote
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### What is meant by the geodesic distance between two points on a rips complex?

I am trying to reimplement this paper and in the surface segmentation section (Section 8 Paragraph 4) of the paper, the author speak of "the geodesic distance in the Rips graph from p to the ...
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### Closed form for simplex homeomorphism

I have a question regarding homeomorphisms from compact convex spaces to the standard simplex. I know that every compact convex subset of $\mathbb{R}^{n}$ with a non-empty interior is homeomorphic to ...
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### Prove a feasible point is optimal for an LP using complementary slackness

Prove that $(2,0,0)$ is the optimal solution to this problem. P) Minimize $2x_1+5x_2+7x_3$ subject to constraints: $7x_1+6x_2+3x_3-s_1=14$ $2x_1+4x_2+5x_3+s_2=4$ Where: $x_1,x_2,x_3 \ge 0$ This ...
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### Interchanged Domain of multiple integral under n-simplex

Suppose that we have a multiple integral under $n$-dimensional simplex as follows: \begin{align*} \underbrace{\int_0^1 dx_n \int_0^{x_n} dx_{n-1} \cdots \int_0^{x_2} dx_1}_{n\text{ times}}\, f(x_i) ...
1 vote
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### How to calculate the volume of the image of a simplex by a general linear transformation??

It is well known that if a linear map $H$ is bijective then we have $$Vol(S)=\text{det}H \, Vol(\mathcal{X})$$ Now I want to know the case when $H$ is a surjective map. How to calculate the volume of ...
I have been given the following question: Given a topological space $X$, for any $x_0 \in X$ we have defined $\varphi_{x_0}:\sigma_1 \rightarrow X: (t_0,t_1) \rightarrow x_0$. Prove that $\varphi_{x_0}... 2 votes 0 answers 11 views ### show that the reverse of the optimization test is not always true using an example We have the following theorem: For a BFS$x^{0}$, if$z_{j}-c_{j} \leq 0, \forall j \in J_{N}$(N is the set of all non-basic variables), Then$x^{0}$is an optimized solution for this problem. Now ... 1 vote 0 answers 79 views ### Intuition for orientation of a simplex (in 3 dimensions) In trying to begin to learn basic homological algebra, i am confronted with orientation of simplices. The definition seems unmotivated and unintuitive: for$n$-simplices with$n \in \{-1,0,1,2\}$, it ... 0 votes 0 answers 23 views ### Covering$n$-simplex with$k$-subsets to produce a lower$m$-simplex,$m<n$? Let vertices of an$n$-simplex be labeled$\{x_1,x_2,...,x_n\}$and let the$k$-subsets or$k$-intersections ($k \leq n$)be identified as$x_{i_1} \cap x_{i_2} \cap ... x_{i_k}=x_{i_1}x_{i_2}...x_{i_k}...
We define a $\textbf{singular$n$-simplex}$ in $X$ to be a continuous map $\sigma:\Delta^n\to X$ where $\Delta^n$ is the standard $n$-simplex. Now, as an example, Let $X$ be a singleton $\{p\}$. Then ...