Approximating chaotic systems

Reply #22

eddessaknight — Sun, 15 Oct 2023 00:50:31 GMT

Nonlinear, yes, but could be curvolinear -JUST LIKE NATURE

Reply #21

ddude003 — Fri, 13 Oct 2023 17:44:14 GMT

You could use a Hidden Markov Model to detect state changes within your lottery time series data... Then use the last change of state as your minimum number going forward... Increment until the next change of state... Rinse and repeat...

Reply #20

Cmoore50 — Wed, 11 Oct 2023 04:46:18 GMT

Test results are posted on the powerball website. Click media center at bottom of page. Then draw results.

Reply #19

Down — Tue, 10 Oct 2023 20:02:27 GMT

I don't know if this will help or not, but in both MM and PB they do two test draws that you don't get to see. So your numbers could have come up in the test draws. The winning numbers that come up are in past draws even the powerball or mega number. So pick 25-30 numbers and 5-10 bonus numbers from the past draws and pick from that pool of numbers and you have a better chance of winning, or you can just Quick Pick.

Reply #18

Cmoore50 — Tue, 10 Oct 2023 12:47:05 GMT

What is the minimum number of past lotto draws to use for prediction? My data is up to 1530 draws. This is for a 5/39 game.

Reply #17

Wavepack — Sun, 24 Sep 2023 13:33:20 GMT

Her paper that you link to is strongly related to the 2nd half of the lecture series. Delayed embedding is used to identify chaotic attractors, stable and unstable fixed points, unstable periodic orbits (with a spectrum of periods), etc. Unfortunately, visual inspection of delayed embedding for lotto ball picking systems has non of these structures that can be visually identified in embedded space. It looks like noise.

2nd order statistics (pairs) covers any information you can pull from a

Reply #16

ddude003 — Wed, 20 Sep 2023 01:10:28 GMT

An interesting find for sure Wavepack... And an interesting direction for sure... https://arxiv.org/pdf/1503.07493.pdf

Oh, crap, the footnotes... Quite the rabbit hole...

Reply #15

Wavepack — Tue, 19 Sep 2023 12:16:45 GMT

Chaotic systems are a subset of nonlinear systems.

The following Nonlinear Dynamics video series by Prof. Liz Bradley , a course funded by the Santa Fe Institute, is worth a watch for better understanding nonlinear systems and practical issues when characterizing them.

https://www.youtube.com/playlist?list=PLF0b3ThojznQ9xUDm-EbgFAnzdbeDVuSz

During the course, she mentions a Nonlinear Time Series Analysis book, which is also worth looking at. The author of that book gave a talk wher... [ More ]

Reply #14

eddessaknight — Sat, 26 Aug 2023 21:33:03 GMT

Modern science Quantum Science says there is no absolute point of certainty outcome in any game, however it does not e laminate HIGHLY LIKELY

Best Wishes

Pro-Player Advocate

Eddessa_Knight w/ LIGHT

Reply #13

ddude003 — Sat, 26 Aug 2023 01:13:19 GMT

If I remember correctly GH was into the financial markets, maybe as commodities trading adviser and a chartist... She used some of these methods in her lottery prediction systems... I think she envisioned lottery history data the same way, as time series data... I even think she embedded some chartist reading/prediction methods into her lottery systems... So, I haven't completely tossed out some of these concepts... Although, I would agree that SARIMAX and ARIMA are not the best tools to use...... [ More ]

Reply #12

hypersoniq — Sat, 26 Aug 2023 00:46:42 GMT

I had found that time series over a mostly uniform distribution tends to return an average when trying to make a prediction. Had hopes for SARIMAX when studying python time series analysis, but the predictions always came out between 4.8 and 5.2 (for pick 3). Then when you see how predictions based on ARIMA are calculated, you realize it was the wrong tool to use

My focus is shifting to classification, though I am not exactly sure what it will look like just yet.

Reply #11

ddude003 — Fri, 25 Aug 2023 01:08:31 GMT

Interesting that you would quote Anais Nin... I would have thought something by Carlos Castaneda, Hunter Thompson, Richard Alpert or Timothy Leary...

Reply #10

eddessaknight — Thu, 24 Aug 2023 00:53:46 GMT

Ancient Chaos echo sidebars worthy of consideration:

In all chaos there is a cosmos,

in all disorder a secret order.

~ Dr Carl Jung, world renowned Swiss analyist

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Anais Nin wrote, In chaos , there is fertility .

-

ORDO AB CHAO

from chaos comes order

-

-

Buono Fortuna (good luck

Reply #9

ddude003 — Wed, 23 Aug 2023 22:10:46 GMT

I have only started to look into this approach myself and haven't found any _good_ reference papers yet... This stuff has to rattle around in the back of my brain for a while before I can start to visualize something that might be of use for my purpose...

Reply #8

Wavepack — Wed, 23 Aug 2023 15:21:21 GMT

I only recently started reading about PRNGs. I was surprised to learn that some PRNGs that are considered cryptographically secure aren't one large cycle in state space, but instead have some short cycles. That indicated to me that if the PRNG was seeded to start in those short cycles, the PRNG wouldn't be random enough.

I'm aware of some satisfiability modulo theory libraries used to solve for the seed given PRNG output. But in those cases, you know the PRNG because it's in the code, and th... [ More ]

Reply #7

ddude003 — Wed, 23 Aug 2023 14:40:21 GMT

I have used stan with limited success... Looking at various ways to integrate it into my quiver of apps... Have you looked into cracking a PRNG with a PRNG

Reply #6

Wavepack — Wed, 23 Aug 2023 03:42:26 GMT

I gave a careful read of the papers. None of the papers that I've read so far help with lotto prediction in any way.

However, the papers show that you can, for a very limited class of chaotic systems, show an equivalence with stochastic input LTI systems, which then allows optimal estimation (ie, prediction) using standard stochastic estimation and filtering techniques.

For example, designing a filter to filter out a chaotic signal in AWGN (additive white Gaussian noise).

Reply #5

ddude003 — Sat, 12 Aug 2023 02:10:33 GMT

Stan as in https://mc-stan.org...

I was a smalltalker... Danny was always fun to talk with... In the mid 90s with his long now clock... And he was one of several very interesting Disney VPs...

Even now not much compares to smalltalking with a lisp... We were supermen...

Reply #4

Wavepack — Fri, 11 Aug 2023 19:22:41 GMT

By stan you mean?

Interesting that Postscript started that early at Xerox Parc.

To demonstrate the Connection Machine CM-2's real time graphical display of computation, we programmed the f(z) = z^2 + c iterative system, z is complex, which generates a fractal (color map to the rate of convergence or divergence) This was around 1988. A quick hack written in *lisp, a parallel form of lisp.

Reply #3

ddude003 — Thu, 10 Aug 2023 15:25:03 GMT

I saw my first fractal on a evans and sutherland graphics workstation in the mid 1980s... A guy from JPL was testing a new pascal compiler and generating fractals, photographing them directly on the e s workstation, for Benoit... BTY postscript has been around since the late 70s before adobe systems at xerox parc...

Have you used stan in your research

Reply #2

Wavepack — Wed, 09 Aug 2023 13:54:29 GMT

Mandelbrot is one of the OG researchers of chaotic systems. He introduced fractal dimension to help characterize chaotic systems. I have two of his books, which I bought while frequenting a used technical book store in the early 90s (before web browsing). The Fractal Geometry of Nature and Fractals, Form, Chance, and Dimensions are the two books. I just quickly scanned them over. I found and quickly looked at chapters 1,2, and the TOC of The (mis)behavior of Markets online. This looks to be earl... [ More ]

Reply #1

ddude003 — Wed, 09 Aug 2023 01:14:59 GMT

The (mis)Behavior of Markets by Benoit B. Mandelbrot and Richard L. Hudson might be an interesting thing... I have always looked at lottery data as time series data... The (mis)Behavior of lotteries have been pretty good to me... So far...

Approximating chaotic systems

Wavepack — Tue, 08 Aug 2023 01:12:23 GMT

Had fun today discovering many wonderful papers on approximating chaotic systems with random input LTI (linear time invariant) systems. Beautiful mathematical insights.

My white ball prediction in MM and PB needs vast improvement, so looking into chaotic systems modeling. Appreciating the research results are motivation enough to read the papers. Solving prediction problems motivated me to discover the papers.

I have found that time variant draw statistics helps a little with megaball