### Author Topic: Real-Time Lossless data compression Histogram algorithm √λ≅X^Y∓Z ∦ λ∈[(ArgMax⇔>∀  (Read 1886 times)

#### xor

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•     • • Posts: 1208 ##### Real-Time Lossless data compression Histogram algorithm √λ≅X^Y∓Z ∦ λ∈[(ArgMax⇔>∀
« on: July 24, 2021, 10:19:27 PM »
Real-Time, Lossless data compression Histogram algorithm

√λ≅X^Y∓Z

λ∈[(ArgMax⇔>∀xω1)→(ArgMin⇔<∀xω9)]

https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols

#### xor

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•     • • Posts: 1208 ##### Re: Real-Time Lossless data compression Histogram algorithm √λ≅X^Y∓Z ∦ λ∈[(ArgMax⇔>∀
« Reply #1 on: July 25, 2021, 01:17:07 PM »
If the event is approached with the logic of finding the most repetitive
The histogram of 32-bit addressing data generates an average of 4gb addressing recommendation.
but keep in mind that not all 32-bit applications actually use 32-bit addressing data, if that were the case.
(32bit apps files were never 4GB in size)

To summarize the subject; You can dump the contents of the repetitive 32-bit data into the 16-bit comparison template.
this is logic It guarantees 50% compression in all aspects.
and secondly, in large data close to 4GB and above
You don't need to create a top list of all data in terms of histogram!
that is, the most repeated from the first order
You can rank first 1000.
the ranking list will contain less data than normal read and write.
« Last Edit: July 25, 2021, 01:25:35 PM by xor »

#### xor

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•     • • Posts: 1208 ##### Re: Real-Time Lossless data compression Histogram algorithm √λ≅X^Y∓Z ∦ λ∈[(ArgMax⇔>∀
« Reply #2 on: December 16, 2021, 06:03:36 AM »
I realize that thousands of people specifically choose TCL to deal with their experimental linux projects,
and I found it very interesting that he read this topic and did not comment

#### xor

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•     • • Posts: 1208 ##### Histogram Based, Real Time Lossless Data Compression Algorithm λ∈[(ArgMax⇔>∀xω1)
« Reply #3 on: April 21, 2022, 10:58:46 PM »
Histogram Based, Real Time Lossless Data Compression Algorithm

only for silicon-based computers : λ∈[(ArgMax⇔>∀xω1)→(ArgMin⇔<∀xω9)]

only for quantum based computers : √λ≅X^Y∓Z

guidebook to understand formulas
https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols

if this formula has not been defined before; may not be limited under any license.
and humanity's common property.
« Last Edit: April 21, 2022, 11:29:09 PM by xor »

#### gadget42

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•     • Posts: 521 ##### Re: Real-Time Lossless data compression Histogram algorithm √λ≅X^Y∓Z ∦ λ∈[(ArgMax⇔>∀
« Reply #4 on: April 22, 2022, 03:09:53 AM »
The fluctuation theorem has long been known for a sudden switch of the Hamiltonian of a classical system Z54 . For a quantum system with a Hamiltonian changing from... https://forum.tinycorelinux.net/index.php/topic,25972.msg166580.html#msg166580

#### xor

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•     • • Posts: 1208 ##### Histogram Based, Real Time Lossless Data Compression Algorithm λ∈[(ArgMax⇔>∀xω1)
« Reply #5 on: April 23, 2022, 01:48:38 AM »

but I couldn't make much sense with the link you suggested.

fascinating https://www.scirp.org/error.html

#### xor

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•     • • Posts: 1208 ##### the spirit of time always whispers something in everyone's ear
« Reply #6 on: May 24, 2022, 01:05:54 PM »
the spirit of time always whispers something in everyone's ear

Quote

If you look at the 8th item on the page;

" x=fwd_f×x[upper]+x[lower]−fwd_cf, "

The similarity with the main topic is very interesting !!!

#### xor

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•     • • Posts: 1208 ##### Histogram Based, Real Time Lossless Data Compression Algorithm λ∈[(ArgMax⇔>∀xω1)
« Reply #7 on: June 17, 2022, 09:48:28 PM »
Benford's law https://en.wikipedia.org/wiki/Benford%27s_law

note:
there is a logical connection with the main topic
« Last Edit: June 17, 2022, 09:51:33 PM by xor »

#### xor

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•     • • Posts: 1208 ##### Re: Real-Time Lossless data compression Histogram algorithm √λ≅X^Y∓Z ∦ λ∈[(ArgMax⇔>∀
« Reply #8 on: April 24, 2023, 05:47:00 AM »
when i asked artificial intelligence to analyze the formula, this came up

Quote
λ∈[(ArgMax⇔>∀xω1)→(ArgMin⇔<∀xω9)]

Sure. The expression λ∈[(ArgMax⇔>∀xω1​)→(ArgMin⇔<∀xω9​)] can be interpreted as follows:

For all values of x, if λ is the argument that maximizes ω1​, then it must also be the argument that minimizes ω9​.

In other words, the expression states that the argument that maximizes one objective function must also minimize another objective function. This is a very strong statement, and it is not always true. However, it is true in some cases.

For example, consider the following two objective functions:

ω1​(x)=x2
ω9​(x)=−x2

The argument that maximizes ω1​(x) is x=1, and the argument that minimizes ω9​(x) is also x=1. Therefore, the expression λ∈[(ArgMax⇔>∀xω1​)→(ArgMin⇔<∀xω9​)] is true in this case.

However, there are other cases where the expression is not true. For example, consider the following two objective functions:

ω1​(x)=x
ω9​(x)=−x

The argument that maximizes ω1​(x) is x=1, but the argument that minimizes ω9​(x) is x=0. Therefore, the expression λ∈[(ArgMax⇔>∀xω1​)→(ArgMin⇔<∀xω9​)] is not true in this case.

In general, the expression λ∈[(ArgMax⇔>∀xω1​)→(ArgMin⇔<∀xω9​)] is true if and only if the two objective functions ω1​ and ω9​ are inverses of each other.