Percentile differences of an arbitrary probability density function https://medium.com/math-simplified/percentile-differences-of-an-arbitrary-probability-density-function-7857d6d4ef42 #ActuarialScience #Statistics #Python #ComputerAlgebra #Approximation

I've found a decent working approximation of π for #PostScript

/pi 0.001 sin 2 div 360000 mul def

Accurate to 7 decimal places. The language uses single-precision floating point, and all its trig routines work in degrees.

This calculates π using the area of a unit radius n-gon, with n=360000

A = ½n⋅sin(360°÷n)

One of Ramanujan's approximations

π ≅ 9801÷(2206⋅√2)

is about as accurate but opaque.

#mathematics #pi #approximation #FloatingPoint

Exploring the Approximation Capabilities of Multiplicative Neural Networks for Smooth Functions

Ido Ben-Shaul, Tomer Galanti, Shai Dekel

Action editor: Murat Erdogdu.

https://openreview.net/forum?id=sWQJfb2GSk

#neurons #layers #approximation

Non-asymptotic approximations of Gaussian neural networks via second-order Poincar\'e inequalities

https://openreview.net/forum?id=BKtxHvwnut

#gaussian #approximations #approximation

Mean-Field Control based Approximation of Multi-Agent Reinforcement Learning in Presence of a Non...

Washim Uddin Mondal, Vaneet Aggarwal, Satish Ukkusuri

Action editor: Marc Lanctot.

https://openreview.net/forum?id=ZME2nZMTvY

#reinforcement #agents #approximation

#CO2 #approximation #climate #ClimateChange #klima #klimakrise #Klimawandel #Klimaschutz
#MLO

Das Diagramm zeigt die Prognose der CO₂-Konzentration am Mauna Loa für April 2023 seit 2000. In 2000 war die Vorhersage 424,84 ppm, dann fiel bis 2003 auf knapp über 422. Ab 2016 stieg die Prognose kontinuierlich bis 2022. Mit den Daten 1958 bis 2022 war der prognostizierte Wert Anfang 2023 422,85 ppm. Der tatsächliche Wert war 422,73 ppm.
1/2

Mean-Field Control based Approximation of Multi-Agent Reinforcement Learning in Presence of a Non-decomposable Shared Global State

https://openreview.net/forum?id=ZME2nZMTvY

#reinforcement #agents #approximation

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Word of The Hour's Annual Survey @ https://wordofthehour.org/r/form

Convert kilometers to miles:

To one half of kms add: 10% of kms, 2% of kms, and half of 1% of kms.

Skip the last addition if you don't need that much accuracy.

[Example results shown rounded to third decimal place.]

#convert #distance #approximation

Convert miles to kilometers:

Add half of the miles and then add 10% of the miles.

Also helps to remember that 400m is a quarter mile.

#convert #distance #approximation

Converting Celsius temperature to Fahrenheit:

1. Double the °C value
2. Reduce the result by 10%
3. Add 32 to the new result

#convert #temperature #approximation

Converting Fahrenheit temperature to Celsius:

1. Subtract 32 from °F
2. Halve the result
3. Add 10% to the new result

#convert #temperature #approximation

(5+1/(63+√8))^(2/3) ≈ (π+e)/2
#maths #math #pi #approximation
Accurate to 8dp or 27 bits!

Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?

Anastasis Kratsios, Behnoosh Zamanlooy

https://openreview.net/forum?id=sNxNi54B8b

#layers #approximating #approximation

Exploring the Approximation Capabilities of Multiplicative Neural Networks for Smooth Functions

https://openreview.net/forum?id=sWQJfb2GSk

#neurons #layers #approximation

#approximation : a drawing, advancing or being near

- French: approximation

- German: die Annäherung

- Italian: ravvicinamento

- Portuguese: aproximação

- Spanish: aproximación

------------

Word of The Hour's Annual Survey @ https://wordofthehour.org/r/form

alright, so my draft is approaching 2000 words. a thread won’t do. I’m writing this as a full essay, reviewing the development of five #numericalmethods for #approximation

But my point about #Phaedrus is succinct enough. By writing down an explanation we’re both practicing explanations and giving a template to rehearse the thoughts behind them. In this non-didactic sense, writing and other information technologies enhance learning “by heart”. But these tools must be used in this manner.

This formula results in a number starting with 3.1415926535897932384626433832... , matching the total of 42863147299 PI digits, and then diverges.

#maths #pi #approximation

Finally the most sophisticated of the three is Simpson’s rule in which pairs of adjacent strips use a #quadratic #parabola to interpolate between the ordinates. This even better at convergence than the trapezium rule. I’ve shown a different function here because for the function shown above the difference between the approximation and the numerical #approximation is not discernible.

#MyWork #Mathematics #Maths #Numerics #SimpsonsRule #FreeSoftware #CCBYSA #Wikipedia #Wikimedia

Totally missed #pi #approximation day (aka #PiApproximationDay) on 22/7. Need to add a reminder in #calendar for next year.
Anyway, nice #read about #irrational #numbers, mentions π in passing:
https://blog.demofox.org/2020/07/26/irrational-numbers/
Found via https://lobste.rs/t/math