google sheets – Locking a formula when adding rows

Currently I have this formula in there

=IF('Form Responses 3'!G$20="","",COUNTIF('Form Responses 3'!G$1:G$167,F20))

It does what I want it to do if I go in a tweak it later, but I don’t want to go in a tweak it

Because it’s a form responses tab, every time a new form is submitted it adds a new row in and my reference cell changes. I’ve done some research and tried out the INDIRECT function (=IF(INDIRECT('Form Responses 3'!G$20)="","",COUNTIF('Form Responses 3'G$1:G$167,F20)), but I can’t seem to get the reference cell to stay G20.

My formula is on a different tab in cell C4.

Predicate Logic translation from English to formula

I am studying for an exam and I have these exercises, I have solved.

Let:
Monkey(x) = "x is a monkey"
Intelligent(x) = "x is an intelligent being"
Likes(x, y) = "x eats y"

  1. No monkey eats a rock.

let Tigers(x) = "x is a tiger"

∀x(Tiger(x) => ∀y¬Eats(y, x)

  1. There exists an intelligent monkey.

∃x(Monkey(x) => Intelligent(x))

  1. Every monkey likes another monkey

∀x(Welshman(x) => ∀yLikes(y, x))

  1. There is only one smart monkey who likes all other monkeys

∃!x(Witty(x) => ∀yLikes(y, x))

I could use some feedback, please.

google sheets – Formula to output the date for next Friday once it has passed 20:00 on Friday

Alsors, try this:

=ArrayFormula(IF((WEEKDAY(TODAY())=6)*(NOW()-TODAY()>=TIMEVALUE("8:00 PM")),TODAY()+7,FILTER(SEQUENCE(7,1,TODAY()),WEEKDAY(SEQUENCE(7,1,TODAY()))=6)))

HOW IT WORKS

The formula assumes Sunday is counted as weekday 1 and, therefore, that Friday is counted as 6.

The first part of the IF checks to see if two conditions are true: That today is Friday and that the current time is greater than or equal to 8:00 PM. If those are both TRUE, then the date is set to seven days in the future (i.e., next Friday).

If this small window of time is not the case, then the second half of the IF statement takes effect. A SEQUENCE is formed of seven dates starting with today’s date. FILTER filters in only those days whose weekday is 6 (i.e., Friday). And since there will only be one Friday within any seven-day SEQUENCE of dates, it will pull whatever the “next Friday” is.

(Note: If today is Friday before 8:00 PM, then the “next Friday” in the SEQUENCE is today, so it stays showing today’s date until after 8:00 PM.)

mathematics – Simple (quadratic) stat growth formula

I’m working on a fairly simple hobby project. It’s an RPG like game and am trying to figure out how to grow stats among different classes. I’ve read several posts about different ways to do this but haven’t quite found what I’m looking for. Usually it’s some sort of exponential growth formula. However I believe if I wanted different classes to scale differently using a formula like that I’d need to play with different formulas for each stat for each class. For instance I may want a tank to scale faster/higher HP than a mage.

In my mind, what I want to do is define a class by giving starting and ending stat values for each stat. So take HP as an example, at level 1 you start at 10 and at max level (say) 100 you end at 500. Another class may start at 10 and end at 350.

I believe what I want to do a quadratic growth curve so while it’s scaling on a curve it doesn’t start as slow as exponential and then ramp up so quickly. In my mind then if I can calculate quadratic growth between 0 and 1, I can multiply that by the total stat growth to get a value at any given level. Problem is I haven’t been able to find a formula to calculate quadratic growth between 2 numbers. Most formulas I’ve seen simply calculates a curve and you get what you get at level 5, 10. Yes you can tweak the growth curve to adjust the stats but to me it makes more sense to get a single growth curve (at this point) and be able to adjust the ending values at each level based on total growth.

real analysis – Proof of Levy-Khintchine formula: Question on the existence of an infinitely divisible distribution defined by the formula

I am reading the proof of the Levy-Khintchine formula from Ken Iti Sato’s Levy Processes, however, I cannot understand a line from the proof that given a symmetric nonnegative definite $d times d$ matrix $A$, and a measure $nu$ on $mathbb{R}^d$ with $nu({0})=0$, $int (1 wedge |x|^2) nu(dx)<infty$, and $gamma in mathbb{R}^d$, we get an infinitely divisible distribution $mu$ whose characteristic function is given by the formula.

In the proof below, it states that $phi_n$ is the convolution of a Gaussian and a compound Poisson distribution. A distribution $mu$ on $mathbb{R}^d$ is compound Poisson if there exists $c>0$ and $sigma$ on $mathbb{R}^d$ with $sigma ({0})=0$ and the characteristic function $$hat mu(z)= exp(c(hat sigma(z)-1)).$$ $D$ here is the closed unit ball.

But I cannot see from below why we get this form for the inner integral. That is, it seems like we should have $int_{|x|>1/n} (1-ilangle z,xrangle 1_D(x)) nu(dx)=1$ from the definition above but I don’t see how we get this. Why does this integral define the characteristic function of a compound Poisson?

enter image description here

python – Computing inverse of modified matrix using Sherman-Morrison formula

I have the following implementation that takes in symmetric matrix W and returns matrix C

import torch
import numpy as np
import time

W = torch.tensor(((0, 1, 0, 0, 0, 0, 0, 0, 0),
              (1, 0, 1, 0, 0, 1, 0, 0, 0),
              (0, 1, 0, 3, 0, 0, 0, 0, 0),
              (0, 0, 3, 0, 1, 0, 0, 0, 0),
              (0, 0, 0, 1, 0, 1, 1, 0, 0),
              (0, 1, 0, 0, 1, 0, 0, 0, 0),
              (0, 0, 0, 0, 1, 0, 0, 1, 0),
              (0, 0, 0, 0, 0, 0, 1, 0, 1),
              (0, 0, 0, 0, 0, 0, 0, 1, 0)))

A = W.clone()    
(n_node, _) = A.shape
nI = n_node * torch.eye(n_node)

# -- method 1
C = torch.empty(n_node, n_node)   

for i in range(n_node):
    for j in range(i, n_node):
        B = A.clone()
        B(i, j) = B(j, i) = 0
        C(i, j) = C(j, i) = torch.inverse(nI - B)(i, j)

As you can see, I have a matrix nI - B and change one element at each loop and compute its inverse. Im trying to use Sherman-Morrison formula to enhance the performance of the code. Here is my implementation:

# -- method 2
c = torch.empty(n_node, n_node)

inv_nI_A = torch.inverse(nI - A)
b = torch.div(A, 1 + torch.einsum('ij,ij->ij', A, inv_nI_A))
inv_nI_A_ = inv_nI_A.unsqueeze(1)

for i in range(n_node):
    for j in range(i, n_node):
        c(i, j) = c(j, i) = (inv_nI_A - b(i, j) * torch.matmul(inv_nI_A_(:, :, i), inv_nI_A_(j, :, :)))(i, j)

I was wondering if I can do further enhancements on my implementation. Thanks!

PS: W is not necessarily a sparse matrix.

Excel 2019 data validation list valid formula

I am trying to create a formula for a drop down list based on a conditional format, where only the cells in G column will be shown if in the column before (the F one) in the same row the cell has some predefined value (cell K4).

When running the formula on a cell and if i press F9 it will the following result (check pic as well)

={"Doc";"Doc";"Doc";"rec 3";"Doc";"Doc";"Doc";"Doc";"Doc";"rec 9";"rec 10";"rec 11";"rec 12"}

However when i place such formula in the Data Validation under the option list it will show only the first result.
The Idea is to create such dropdown with the use of a direct approach and not with the use of third cells where i will have the place the result on them.

This is the formula

=OFFSET(F1,IF( ((F2:F14=K4))*ROW(F2:F14) = 0, 0,( ((F2:F14=K4))*ROW(F2:F14))-1),1)

I have try as well placing the INDIRECT formula on it but it gives an error… Not sure what else i can do…
enter image description here
Thanks in advance

Excel formula to skip the rows with zero value while linking

I need a small help in fixing my formula.
i have a report from erp with few employees name and the amount they owe. It is a dynamic report and changes everyday.
My requirement is that I need a formula to link with employees who has a balance only

In the below screenshot column D shows the balance and i wrote a formula to bring the values =IF($D2>0,B2,””)
My objective is avoid blanks with out using filter. Is there a dynamic formula to fix this.
enter image description here

maxima minima – Morphological Closing. Formula understanding

I am trying to do use the morphological closing operation on a greyscaled image. As I found out closing is a combination of dilation and erosion.
Now I am trying to understand the formulas of dilation and erosion.
The formula of dilation is
$$
left( A bigoplus X right)left( x,y right) = max left{ A left( x+s,y+t right)+ Xleft(s,t right) right}
$$

I dont unterstand what s and t should be? Is it a max over s and t? And s and t are coordinates of image pixels? But if so, is it a max over the whole image or just over the neighborhood of (x,y)?

custom list – SharePoint Validation Formula help needed

I need assistance with a validation formula for a list with 5 content types and 5 different outcome columns and I want to force the user to choose and outcome when the outcome date is chosen and vise versa. the Outcomes are: ETOutcome, STOutcome, TTOutcome, MTOutcome, TCOutcome. I also want to not allow an outcome to be chosen when the status of the item is pending. Any help would be appreciated.