## fitting – Help setting the weight of the NonlinearModelFit to 1/(y + y_fitted)^2

I’m trying to use Mathematica’s `NonlinearModelFit` function to find a best fit for data collected that follows the equation`y=aExp(-bz)`, where a and b are the fitting parameters, and z is the variable. So I have many measured y values for several z values, but the fit I obtain when using the `NonlinearModelFit` is not quite what I expect it to be. From my understanding, the default weight for each data point is equal, and the standard error is calculated using `(y_i - y_i,fitted)^2` for every data point. I would like to use the weight `1/(y_i+y_i,fitted)^2` so that each data point is weighted more equally. I understand the use of the example `LinearModelFit(Range(10)^2, x, x, Weights -> (Sqrt(#2) &)) // Normal` from https://reference.wolfram.com/language/ref/Weights.html where I can incorporate the value of `y_i`, but I’m still just not sure how to implement the value `y_i,fitted` into the weights, if it is possible. Any help would be appreciated, thanks!

## mysql – How to write a query to get wine pairing for a pizza based on pairing weight

I am working on a query to pair drinks to pizzas.
Currently I am able to show the pizza_name, beverage and the pairing_weight being the amount of toppings on a pizza that the beverage pairs with.
From here, I am looking to just output a mapping of distinct pizza name to beverage.
I am unsure how to format the query to just return the top result per pizza based on pairing_weight.

``````mysql> select pizza_name, beverage, COUNT(beverage) as pairing_weight
-> from pizza_production
->     JOIN pizza_restrictions pr on
->         pizza_production.topping_name = pr.topping_name
->     JOIN beverage_pairing_notes on
->         restriction = pairing
->     GROUP BY pizza_name, beverage
->     ORDER BY pizza_name, pairing_weight DESC;
+--------------+--------------------+----------------+
| pizza_name   | beverage           | pairing_weight |
+--------------+--------------------+----------------+
| Grand Padano | Prosecco           |              2 |
| Grand Padano | Champagne          |              2 |
| Grand Padano | Riesling           |              2 |
| Grand Padano | Cava               |              2 |
| Grand Padano | Pinot Noir         |              1 |
| Grand Padano | Carlsberg beer     |              1 |
| Grand Padano | Zinfandel Rosé     |              1 |
| Grand Padano | Chardonnay         |              1 |
| Grand Padano | Chenin Blanc       |              1 |
| Grand Padano | Gewürztraminer     |              1 |
| Grand Padano | Guinness beer      |              1 |
| Grand Padano | Pinot Grigio       |              1 |
| Grand Padano | Heineken beer      |              1 |
| Grand Padano | Irn Bru            |              1 |
| Grand Padano | Malbec             |              1 |
| Grand Padano | Muscat Blanc       |              1 |
| new york     | Riesling           |              2 |
| new york     | Champagne          |              2 |
| new york     | Prosecco           |              2 |
| new york     | Pinot Noir         |              2 |
| new york     | Malbec             |              2 |
| new york     | Syrah              |              1 |
| new york     | Cava               |              1 |
| new york     | Cabernet Sauvignon |              1 |
| new york     | Chardonnay         |              1 |
| new york     | Carlsberg beer     |              1 |
| new york     | Chenin Blanc       |              1 |
| new york     | Gewürztraminer     |              1 |
| new york     | Guinness beer      |              1 |
| new york     | Muscat Blanc       |              1 |
| new york     | Heineken beer      |              1 |
| pepperoni    | Pinot Noir         |              3 |
| pepperoni    | Malbec             |              3 |
| pepperoni    | Muscat Blanc       |              2 |
| pepperoni    | Heineken beer      |              2 |
| pepperoni    | Guinness beer      |              2 |
| pepperoni    | Gewürztraminer     |              2 |
| pepperoni    | Chenin Blanc       |              2 |
| pepperoni    | Riesling           |              2 |
| pepperoni    | Carlsberg beer     |              2 |
| pepperoni    | Cabernet Sauvignon |              2 |
| pepperoni    | Chardonnay         |              1 |
| pepperoni    | Champagne          |              1 |
| pepperoni    | Prosecco           |              1 |
| pepperoni    | Cava               |              1 |
| pepperoni    | Rioja              |              1 |
| pepperoni    | Syrah              |              1 |
| pepperoni    | Zinfandel Rosé     |              1 |
| vegetarian   | Diet Coke          |              2 |
| vegetarian   | Prosecco           |              1 |
| vegetarian   | Champagne          |              1 |
| vegetarian   | Riesling           |              1 |
+--------------+--------------------+----------------+
52 rows in set (0.01 sec)
``````

An example of desired output would be

``````+--------------+--------------------+
| pizza_name   | beverage           |
+--------------+--------------------+
| pepperoni    | Pinot Noir         |
| new york     | Riesling           |
| Grand Padano | Prosecco           |
| vegetarian   | Diet Coke          |
+--------------+--------------------+
``````

Is there a way to pull this data from what I already have in the output of the query above?
Thank you.

## quantum mechanics – Beam Splitter Toy Model History Weight Calculation

Given this modern of a beam splitter (see picture), and the two possible histories:

Yc = (0a) • (1c) • (2c) • (3c) • (4c)
And
Yd = (0a) • (1d) • (2d) • (3d) • (4d)
for f=4,

how do I calculate the weight of history Yc and Yd. I know Yc=Yd=0.5, but how do I calculate this? I hope I have provided enough information to answer this question. The material comes from Robert Griffiths “Consistent Quantum Theory” pg. 140-142.

Thank youbeam splitter toy model

## python – Initialize weights in pytorch with customized weight?

I want to initialize the weights of my neural network with parameters samples from a specific distribution, that is not already present in nn.init module. Let’s say for example a beta distribution.

I saw that you can use the method described there: Custom weight initialization in PyTorch

But there you need to use the nn.init. What is an elegant way to initialize weights from a distribution that I specify

## algorithms – Sorting n weight disks with decision tree

I was refreshing some old tests about sorting algorithms, there was a question as follow:

Question: we have `n` weight disks with different weights and we want to sort them pair by pair, How many times we have to weight in worst case (maximum comparisons) to sort the whole disks?

the answer was $$lceil logn! rceil$$.

My issue is that I could not get to the answer and could anyone elaborate on how the answer is working?

Also one of the options was $$lceil nlogn rceil$$, and as we know,
the order of $$logn!$$ and $$nlogn$$ are same, So why shouldn’t the
ceilings be equal too?

and How does having an ordered and distinct set of size `n`, matter in decision tree?

## algorithms – 0/1 Knapsack problem with minimal weight

so i have this problem where:

• I have to accomplish a challenge with n quests. Each quest gives me:

1. p points and
2. needs t time to be done.
• The object is to complete the challenge that needs M points to be completed, in the least possible time.

So let’s say i have these following quests:

q1 => p1=20, n1=5

q2 => p2=40, n2=20

q3 => p3=10, n3=2

q4 => p4=30, n4=6

I want to solve this problem for M = 50.

I could solve q2 and q3 in time 22. I will get the 50 points, but it’s not the optimal solution since solving q1 and q4 will also give me 50 points in time 11.

I know that this is a knapsack problem but i just can’t figure out how i am suppose to store in my table so i can get a result the set of quests that have to be done in order to have the least possible time. I need to find a dynamic programming algorithm which will be able to find the answer. If someone knows how my data structure should look like and how i should store the data inside, generally what idea should i follow in order to solve this problem, i would really appreciate help since i’ve been stuck and i don’t know how to solve it.

## Command for finding maximum weight Hamiltonian path between two vertices

A Hamiltonian path is a graph path between two vertices of a graph that visits each vertex exactly once.
Finding a single Hamiltonian path of a graph $$g$$ is implemented in the Wolfram Language as FindHamiltonianPath[$$g$$]Hamiltonian path.

What command could be used to find the Hamiltonian path with maximum path weight between the starting vertex $$s$$ and the terminating vertex $$t$$ in the following edge labeled graph?

## 8 – Shipping weight not calculated?

we are currently trying to get our drupal commerce 2 attaching a certain shipping method based on the weight of the order. It is pretty simple (at least I thought so): if the order is below 20kg, it is one rate, above a second rate.

Here is what I did:

• enabled commerce shipping module and physical fields
• added a custom physical weight field field_prod_gewicht to the default product type (the only one we have)
• marked the default product variation as shippable
• filled the individual products with their weights accordingly
• created two shipping methods with different prices, only restricted by Shippment Weight

So far so good – on the shipping page I see indeed only the lower rate shipping method, but if i adde more weight to the order, the higher rate shipping method never appears.

My suspicion is, that the weight is not calculated at all, or that there is some kind of implicit convention I did not follow.

Anybody has an idea, how to solve or debug this?

Thx a lot!

## air travel – If a flight ticket indicates that the maximum luggage weight is “50 lb/23kg”, is the limit 50lb or 23kg?

23kg = 50.7 lb. I know that typically the check-in counter agents would allow check-in luggage to be above 1 lb the maximum free authorized weight, but just in case some agent decides to strictly apply the luggage weight policy.

If specific to the airline, I’m currently interested in Qatar Airways. If specific to the departure airport, I’m currently interested in SFO.