Tuesday, August 18, 2020

Leibniz Wrong About Dice!

 

Leibniz Wrong About Dice!


I was reading a book about Leibniz called “Selections” and then “I, Claudius” by Robert Graves. Emperor Claudius wrote a small pamphlet about throwing dice. Leibniz had a small section about dice odds—that he was using to illustrate some other matter.

 

Two dice references in two different books got me thinking.

 

Leibniz got something wrong! He wrote about someone throwing two six-sided dice and rolling an “11”, and he wrote that there was only one way to roll an “11”.

 

Technically, there are two ways to roll and “11”: you can either roll 5 & 6…but you can also roll 6 & 5. Each die has a different outcome.

 


TWO SIX-SIDED DICE WAYS TO THROW EACH NUMBER


2 = 1+1

3 = 1+2 or 2+1

4 = 1 +3 or 3+1 or 2+2

5 = 1+4 or 4+1 or 2+3 or 3+2

6 = 1+5 or 5+1 or 2+4 or 4+2 or 3+3

7 = 1+6 or 6+1 or 2+5 or 5+2 or 3+4 or 4+3

8 = 2+6 or 6+2 or 3+5 or 5+3 or 4+4

9 = 3+6 or 6+3 or 4+5 or 5+4

10 = 4+6 or 6+4 or 5+5

11 = 5+6 or 6+5

12 = 6+6

 

As you can see, there are more ways (easier) to roll a “7” than any other number. Lucky Seven! 


When Leibniz made his error, he stated there was only one way to roll an “11”. But as you see, there are two ways, which makes “11” easier to roll and “2” or “12”—and the same odds as rolling a “3”. That’s a pretty significant difference-that makes the chances or rolling an “11” 5.56% instead of only 2.78% which is double the odds.


Scribbled notes on an old library catalog card I was using as a bookmark:





Claudius was never as dumb as he pretended to be.


Tuesday, May 26, 2020

Sacred Monster! A Zapotec Bat-God.




Sacred Monster! A Zapotec Bat-God.






PRE-COLUMBIAN BAT GOD TERRACOTTA FIGURE [MDL206.700.00]
4.75" (12 cm) high x 2.5” (6.3 cm) wide x 1.25” (3.1 cm) depth.
Zapotec, Monte Alban area, Mexico from the Oaxaca Valley.
400 A.D - 600 A.D. (city of Monte Alban Phase 3 200 A.D-900 A.D.)
Mold-made terracotta standing figure of the Zapotec Bat God. 
Perforated eyes, belted loincloth, crest atop head, moderately concave back.



This piece traces its provenance to the prestigious Sotheby Parke Bernet NYC Galleries. Listed in auction catalog PB84 Sale Number 523, December 7th, 1976 “Pre-Columbian, African, Oceanic and American Indian Ethnographic Art and Antiquities. Various owners including property from the private collection of Helen S. Wilbur”. Listed as “Item 41. Zapotec Terra Cotta Figure of the Bat God, C./400-600 A.D. 1976.”

The Zapotecs of the Oaxaca Valleys area of what is now southern Mexico got their start around 700 B.C. A little afterwards a large settlement called Monte Alban was constructed above the valleys. The Zapotec called themselves “the cloud people”. There are still a few hundred-thousand speakers of various Zapotec dialects.


A little (not yet fully cited) background on this little beast. It’s a bat. Although, many times Zapotec and Mayan jaguars turn out to be bats. But since there are indications of blood and sacrificial themes (see below) we’re calling this a bat. Like 95% sure. Similar items include holes and mouthpieces so the figure could be used as a whistle—this one is not a whistle. Extremely similar to Zapotec funerary urns—both there’s no bowl or urn on its back.




WHERE

The Mesoamerican bat god entity took a few different forms. Of interest to this piece is the bat god Camazotz (cama-death, zotz-bat in the K’iche’ language). Camazotz is the god of night, death and sacrifice. Kʼicheʼ (or Quiché) is a Maya language of Guatemala that to this day the second most widely used language in Guatemala after Spanish. According to Sotheby’s Parke Bernet Gallery this piece originates a little farther north, from the Monte Alban area (six miles from modern-day Oaxaca City) of the Oaxaca Central Valleys region.








SACRIFICE

Although a Zapotec god, this piece shows later Mayan glyph on its chest denoting “blood” in the stylized form of a blood droplet. On either side of the mouth are glyphs that may denote the heart glyph, meaning “sacrifice”, in particular sacrifice via decapitation and/or the cutting of the victim and the removal of the still beating heart. In the Oaxaca Valley area of southern Mexico bats are found on Zapotec funerary urns [Caso & Bernal 1952: 67-68]. Bats of the divine/sacrificial kind are commonly portrayed with facial designs denoting sacrifice on their cheeks and/or temples [Thompson 182].




THE ONE TRUE BAT GOD CAMAZOTZ?

One popular legend has Camazotz tricking two hero brothers into a journey through the underworld. While hiding, one brother sticks out his head which is immediately ripped off by Camazotz and taken to be used in the “ball game” of the gods. Real humans (generally prisoners of war) were forced to play this ball game, with the losers being sacrificed and decapitated. Although this bat may have been a different bat than Camazotz.




NOT ALWAYS CAMAZOTZ!

Early research led to any and every bat being identified as a death-bat-god, whereas recent research suggests that bats can symbolize: messengers (similar to winged Mercury), vegetation and agricultural fertility, or even personifying diseases [Brady 2016, 227-237]. The proper interpretation of the (single) story of hero twins portrays the bats as numerous—the underworld (Xibalba) contained a “house of bats” where the decapitation took place. Bats—plural!

Bats among the Pre-Columbian Mesoamericans could be just bats; bats symbolizing things; divine or at least supernatural bats symbolizing things; humans with bat wings and/or heads; various gods; or even the bat-god himself “Camazotz”. In fact, it was a messenger bat working on behalf of the god Tohil (a weather and fire divinity) that demanded bloody sacrifice in exchange for giving fire to mankind—not Camazotz.


The fourth month (out of eighteen) in the Mayan calendar is “Zotz”. Twenty-year time periods, called Katuns, where separated in Mayan calendar writings with an upside-down bat glyph. This use of the bat glyph appears to have started being used in the late 700s A.D. [Berlin 1964: 1-7].



 




BLOOD

God “Q” of the Maya has been associated with the number 10, bats, death and was the god of human sacrifice. Bat glyphs appear with the “cauc” symbol of circles or bunches of grapes, which alone usually stands for storms, rain, gods, the divine. When used with the bat it may confer divinity (Camazotz himself) or possibly a rain of blood (very bloody human sacrifice). A harvester of blood? Or maybe agriculture?


The extreme bloodiness in the form of self-mutilation and blood-letting itself was a specific goal. Mayan priests/royalty would pierce their tongues or earlobes to draw blood. The bat god appears on the pyramid of Acanceh twice with symbology mimicking the god of rain [Blaffer 1972: 60-61]. Again, raining blood? Maybe not, here it could be the agricultural aspect of the bat—often depicted with a hummingbird—that is being shown. Ruling elites would practice bloodletting, let the blood fall on bark paper and then burn it as an offering to the gods, who themselves shed blood to create man. Men and women are shown piercing themselves or drawing a barbed rope through their earlobes or tongues to shed their own blood—lots of it!

Bats are commonly depicted with a prominent leaf-nose that imitates an obsidian sacrificial dagger. Often the bat is wielding an identical dagger, holding a victim by the hair or even ripping out a human heart. Generally only prestigious prisoners of war were used for direct sacrifice via knife. It is said that the armpit-to-waist area of humans belong to the gods, meaning the area cut open to remove the sacrificial victim’s heart. Even today, with anesthesia and modern pain killer, a thoracotomy (for removing portions of cancerous lungs) is considered one of the most severe medical procedures in terms of post-operative pain. It was a quick, but not at all pleasant way to die.




RANDOM

The Mayan metaphor zutz atax I wut reads as “heavy-faced or bat-faced” meaning someone who is so tired their head is nodding forward, like a bat sleeping hanging upside-down [Aulie, 1951].


There is the oft cited story of the Zotzil Mayans living in Chiapas along the modern Mexican-Guatemala border who found a bat statue and worshiped it as a god, adding it to their other divinities [Ximenez 1929-31: Vol. 2, Ch. 48).





TERRACOTTA AND MAGNETS

This piece is terracotta. Terracotta usually contains magnetite, and when it is fired to a high heat and then cooled slowly the magnetite crystals orient and can become slightly magnetic. So, I tested this statue with an Gauss / EMF meter but the results were too low to register on my simple unit. Next I tried some extremely powerful rare earth magnets (N42 and N52, 13,200 Gauss+) and they actually stuck/repelled from the statue! To be clear: these are very expensive and dangerous rare earth magnets, the kind that if you stuck them to your refrigerator you would need pliers to pull them off of it. And they barely reacted, but they did stick weakly.

So, is this a cast metal statue? Well, if it where are ferric metal like cast iron or steel the magnet would have crushed my fingers against the statue. Also, the statue is way too light in weight to be those. How about aluminum? Well, magnets don't stick to aluminum, but if there are enough impurities (like in some beer cans) and you use a strong enough magnet (like rare earth magnets) you can get the mostly aluminum item to react. However: the statue doesn't feel the correct weight to be aluminum; it has a very glass/pottery like sound when tapping on it; it flakes and powders when an extremely fine blade tip is poked into it. In fact, this is basically how ceramic (non-metallic) magnets are now made in factories every day.

Also, Mesoamericans have been found to use magnetic "lightening stones" in their statues. Some rocks become magnetic after being struck by lightening. I found a citation (but lost it at the moment) that records Mayan clay effigies with small magnetic stones embedded in them. Particularly the facial areas. Where does this bat-god react the most? Right in his cute little snout! Also near the bottom edge of the loincloth. A series of large pot belly head statues made by the earlier Olmec peoples that taken from Monte Alto and moved to the city of La Democracia in Guatemala have been found to contain magnetic areas--a team from Harvard has been mapping out their magnetic fields. Here's a nice link directly to Harvard so you know this isn't a conspiracy theoryhttps://news.harvard.edu/gazette/story/2019/07/harvard-study-reveals-ancient-mesoamericans-knowledge-about-earths-magnetism/ 

The magnetism of the pot belly statues is focused around the cheeks and belly. Although, much like our bat-god here, that could just be the sharp edges of the statues being more magnet--rather than a conscious effort to localize magnetic materials by the original makers. Also, it could just be naturally occurring in the original materials.

Later on the Maya were still playing around with magnetic materials in the form of iron-ore mirrors made of lodestone, iron pyrite, etc. 

And of course in Chiapas Mexico, specifically the ancient Mayan site called "Izapa" there is the famous turtle sculpture that is a huge magnet. You can visit Tapachula and go see the turtle, he'll make your compass spin. Professor Alberto Passos Guimarães has written about Mesoamerican magents, although mostly physics papers, although his "Mexico and the early history of magnetism" is an easy read.


Gamma Spectrometer Fun

Two different sets of gamma spec run. One gave me a spike at the Protactinium line. Protactinium is in soil, loam and clays. So the clay was made from clay. Learned nothing.







The other run with different voltages, calibration and probe showed Manganese. The Central Tlacolula area has clay low in Manganese; the Western Valle Grande area is relatively high. However, my system isn't in the same league (or calibration) so this also tells me nothing.

The hints of cobalt didn't illuminate matters either.




CITATIONS (NOT COMPLETE-ROUGH DRAFT)

Aulie, E. & Aulie, W. 1951. Palencano Chol-English Vocabulary. Ms. Mexico: Instituto Linguistico de Verano.

Berlin, H. 1964. El glifo ‘zotz invertido’. Antrop. Hist. Guatemala 16, 1-7.

Brady, James E. Bats and the Camazotz: Correcting a Century of Mistaken Identity. Latin American Antiquity. Volume 27, Issue 2, 2016.

Guimaraes, A. P. Mexico and the early history of magnetism. Rev. Mex. F´ıs. E 50 (1) (2004) 51–53; June 2004.

Thompson, J. Eric S. Maya hieroglyphs of the bat as metaphorgrams.

Ximenez, F. 1929-31. History de la Provincia de San Vicente de Chiapa y Guatemala de la Orden de Predicadores. 3 volumes. Guatemala: Soc. Geog. E History.






Rrrrrr...if I gnaw a couple of my arms off I'll look like a bat too!

Tuesday, May 12, 2020

What is a colonoscopy like?





What is a colonoscopy like?


Short answer: totally not bad at all!

I had a have a colonoscopy and was enraged when everyone I asked about it who had one before would answer “it’s totally no big deal!” 

I was like, “Are you insane? They shove a camera in there!!!! How can that not be a big deal?!?!!?”


Well, it wasn’t a big deal.




LITERALLY (NOT FIGURATIVELY) OVER A GALLON!

I was given a prescription for laxative. It was powder and a big plastic jug that was a little over 1 gallon. Add water to the jug and powder and you’ve got literally over a gallon of laxative to drink.

I added the water and mixed it up like the instructions said and then took 16 red disposable plastic party cups and filled them up. I was going to ease of drinking. I had to do this because my powder as not flavored. I’ve heard people get cherry or pineapple. Mine was unflavored and I gagged just smelling it. That freaked me out: how can I drink 16 of these cups when I can’t even smell it without gagging loudly?

Anyway, I commenced to drink liquids throughout the day and not eat anything. Lots of liquids. Water and arctic cherry Gatorade (which is a clear drink—no red or colored drinks allowed). I had to drink one bottle per hour, so I made sure to stock up and get a bunch of bottles.

Now, my procedure was set for first thing in the morning, so the instructions were to drink a bottle of liquid every hour on the hour, then at midnight drink 8 cups of laxative; then at 3:30am drink the other 8 of the cups of laxative. Each cup had to be swilled down with a 15-minute break in between. It was extremely difficult to do because of the horrible taste (like salty used dishwater). I would drink half a cup while holding my nose, gag, sip a little Gatorade, then finish the cup. Repeat every 15 minutes until all 8 cups, then the other 8 cups were all gone.



So, what happen with literally more than a gallon of liquid laxative on an empty stomach? Nothing. I could feel my stomach sloshing around when I walked (which was actually probably the liquid being retained in the colon). It felt like I filled a plastic shopping bag with water and strapped it to my belly. Nothing happened, and I went to bed and dozed off.

Around 5am I woke up and still nothing. I actually was using the bathroom less than normal (and normal was bad—thus the need for the colonoscopy). Finally, I was so worried because I new I had an early appointment I got up and walked around the house a few times. Then it hit me and I ran to the restroom. All 1.1 gallons swooshed out without any cramps or even trying. It was totally painless. Again, when you’re used to going 7-9 times a day and it’s unpleasant, this experience was really nice.

After sitting there for quite a while and then showering I took another nap.





THE PROCEDURE

I woke up and showered again and dressed in a track suit. Then I was driven by a family member to the doctor’s office. Super nervous time!!!!!

I went into the office and was immediately ushered into the prep room. A nurse told me to take all my clothes off except socks and put them into a big plastic bag. Then put on a gown. I did this and she returned and had me lay down.

She took my blood pressure and pulse. Then she put a catheter into the top of my hand. This is a needle with a plastic thingy so that any other needles (the anesthesia) gets plugged into the catheter instead of using more pokey needles. The catheter was taped down to the top of my hand with medical tape.

Then she said, “OK, it’s time to wheel you into…THE PROCEDURE ROOM”. At which point I almost threw up I was so nervous. Luckily my stomach was empty. Also I only had socks and a hospital gown on so I couldn’t run away.

They wheeled me laying down into the Procedure Room and a new lady (who was the anesthesiologist) said hello and that she would be monitoring my heart and breathing. She took my blood pressure and pulse and then said, “OK, lie on your side”; and I thought: Oh man, here it comes. But nothing happened. She was just monitoring how my blood pressure changed while lying on my side. Then she said lay back down and monitored everything some more.




IT BEGINS

After a little while of this she said, “OK, I’m going to start the medications now”. Then she plugged some IV lines into the catheter thingy and flipped a switch.

I looked at my hand and she asked if anything was wrong. I said “No, I just felt a little pinchy feeling, but I think it’s just the tape on the catheter pulling the hair on the top of my hand. No biggie.”

She laughed and said that it might actually be the medicines. Then she handed me my shoes.

You read that right: they started the medicine; I felt a tingle in my hand--and they handed me my shoes. I looked down and I was already dressed (minus shoes).




IT ENDS

For a split second before I looked down at my feet I saw the catheter taped to the top of my hand, and then it blinked and turned into a bright neon green bandage. That was moment in-between. The started the medicine; I looked at my hand; I blacked out; they did the procedure; I got dressed; and they handed me my shoes as I was starting to become truly conscious. Neato!

I was about to yell “you made me drink all that horrible tasting laxative and you’re not even going to do the procedure?!?!?” but then I thought, “these idiots didn’t do the procedure but think they did, now’s my chance to sneak out of here!!!!”

Then it occurred to me that I wasn’t on the table and was fully dressed and in some other room so they must have done the procedure. Woah! No falling asleep and no waking up. It was just a blink and you’re dressed and leaving.

As I was holding my shoes and marveling at how cool it all was my ride peaked into the room and said “what are you doing? Put your shoes on and let’s go!”

I said “OK, yeah…um, I’m hungry let’s get burgers on the way home!”

A split second later we were at the order window at Wendy’s ordering a Bacon Burger. We started to pull up to the payment window and all of a sudden, BAM:  I was standing in the living room and my burger all eaten up and my drink half gone! I was like “who the heck ate my food!” I did, I just didn’t remember. It was a sliding wall of amnesia for about an hour.

My ride asked if I remembered talking to the doctors and nurses. I said no! What about the juice and cookies? I said, “someone must have stolen them because I didn’t get any juice or cookies!” My ride said that they sat with me while I ate them. Woah! Amnesia!

A few days later I did remember being bundled up with my feet near a window. Is this a false memory or just a slice of what really happened? A long time later and I haven’t remembered anything else.





WRAP UP

So what’s a colonoscopy like? They turn on the medicine, then you’re magically dressed and leaving. A time machine. It’s not like on TV were the screen fades to black and then fades to light again. It’s like that old TV show Bewitched: a twitch of the nose and the whole room and circumstances instantly change (and you get to leave immediately).

No falling asleep. No waking up. Just a literal blink of an eye and you’re leaving the room.


FYI: in the visit before the colonoscopy my doctor asked “how sedated” did I want to be. I was like: 100% please! They said for 100% they’d have to reschedule and do that downtown at the bigger hospital, so instead they would do like 90-95%. Man, it was like 100% x a thousand!


The take away: if the government offered to pay me the same salary I make now, but instead of going to work I’d have to get a colonoscopy once a week--I’d seriously consider it. It’s that not bad.





 "I'm still nervous! Meow!"

                                                              Don't be, it's no big deal.

Monday, December 23, 2019

Getting high voltage power from a relay and 9v battery



Getting high voltage power from a relay and 9v battery


So, I wanted to power a neon NE-2 bulb. Just as a test. It takes about 95v to make the bulb light up.




I didn't feel like pulling out a huge power supply and setting things up. I stumbled across an easy relay type power supply.

This will supply continuous power or light, if you use two pins for the + leg of the bulb and two for the - side. However this is just a fun goof. The first part is just testing the relay and getting a single blink of light. Scroll to the bottom for the continue light.

All that's need to create 100v-200v is:

-A normally closed (NC) 5v relay that has a metal core and nice big wire windings.
-9v square battery
-Something to power/test, in this case an NE-2 neon bulb.

Smaller Reed relays also work!


Hopefully your relay will have nice, simple +/- markings on it like mine did:






I just wrapped the legs of the bulb onto the + and - pins. One leg around + and the other around -.







Then you just run wires from the square 9v battery to the correct legs:










I simplified it even further by getting rid of the black and red wires: I can just touch the battery terminals to the legs of the neon bulb and the relay fires and the light blinks:



In the above photo the two middle pins of the relay are + and -. I just wrapped the legs of the neon lamp bulb around them (didn't even solder).


If you reverse the +/- the light bulb lights up, but the relay doesn't click open and closed. If you use it the correct way and have a really loose touching of the wires and battery the relay will open and close so fast it will vibrate while blinking the light.

If you make a strong connection it will only blink once and then the light will go out.

This shorts out the battery so I didn't want to play with this connected too long. This would blow up an actual power supply!

I could probably insert this relay into any of the previous oscillating circuits I've built and have it fire this 100v bulb. Kind of nice to be able to easily use a beefy neon bulb instead of a dorky LED.

What's going on? How can a 9v battery give you over 100v?

The tiny voltage enters the relay and opens it; the magnetic field then collapses in the coil causing inductive kick-back of the higher (200v?) voltage; repeat.


Here is a newer Reed relay I pulled out of a broken PA system amplifier someone have me:


It made the light bulb blink, but even less than the bigger relay. Now, here's a trick to make it continuously power the bulb and the point of this post:


All you do is use all four pins for the bulb and add the power from the battery to the opposite side's corner pins. That feeds the power backwards through the relay.

Here's the pin-out for this relay:


The pins are numbered oddly. There are only 8 pins but the numbers aren't 1-8, LOL!

Pin 2 and 4 get one leg of the neon bulb.

Pin 5 and 7 get the other leg of the neon bulb.

Yes, two pins per bulb leg at the same time.

Positive battery to pin 11.
Negative battery to pin 14.

It will oscillate (vibrate) and light the bulb. It will actually blink it off and on very quickly (and loudly). 

If the light just blinks, reverse the battery posts.

The Reed type newer relays won't light the bulb! They will oscillate though.


Wednesday, December 18, 2019

Chua Circuit Bibliography


Chua Circuit Bibliography 
(working links as of 12/18/2019)


I'm continuing with oscillating circuit experiments. More inductors are being delivered in the next few weeks. This is a list of Chua Diode and Circuit articles with working (free) links. Some are pretty advanced and focus on equations and synchronization--the earlier the year of publication the more physical circuit-based (fun) it will be if you're building your own circuits and playing with oscilloscopes or LTspice:


·          Aguirre, L.A. [1995] "The use of identified models in the control of a chaotic circuit," 1995 IEEE International Symposium on Circuits and Systems (Cat. No.95CH35771). IEEE. Part vol.2, pp.1528-1531.
·          Aguirre, L.A., Souza, A.V.P. [1998] "An algorithm for estimating fixed points of dynamical systems from time series," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.11, pp.2203-2213.
·          Aguirre, L.A., Torres, L.A.B. [1997] "Fixed point stability analysis of Chua's circuit: a case study with a real circuit," Journal of Circuits Systems & Computers, vol.7, no.2, pp.111-115.
·          Aissi, C., Fadul, F. [1997] "Chaos in conditionally reset linear systems," Journal of Circuits Systems & Computers, vol.7, no.3, pp.177-189.
·          Alexeyev, A.A., Osipov, G.V., Shalfeev, V.D. [1995] "Effects of square-wave modulation on CNN patterns," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.700-705.
·          Algaba, A., Freire, E., Gamero, E., Rodriguez-Luis, A.J. [1999] "On the Takens-Bogdanov bifurcation in the Chua's equation," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E82-A, no.9, pp.1722-1728.
·          Altman, E.J. [1993] "Normal Form Analysis of Chua`s Circuit with Applications for Trajectory Recognition," IEEE Transactions on Circuits & Systems II-Analog & Digital Signal Processing, vol.40, no.10, pp.675-682.
·          Alvarez, J., Alvarez, J., Velasco, M. [1997] "Approximate model-matching for nonlinear systems with a small time-delay; application to a chaotic Chua circuit," Proceedings of the 36th IEEE Conference on Decision and Control (Cat. No.97CH36124). IEEE. Part vol.2, pp.1631-1636.
·          Anishchenko, V.S., Kapitaniak, T., Safonova, M.A., Sosnovzeva, O.V. [1994] "Birth of double-double scroll attractor in coupled Chua circuits," Physics Letters A, vol.192, no.2-4, pp.207-214.
·          Anshan, H. [1988] "A Study of the Chaotic Phenomena in Chua's Circuit," Proceedings of 1988 IEEE International Symposium on Circuits and Systems (Cat. No.88CH2458-8). IEEE. vol.1, pp.273-276.
·          Arena, P., Baglio, S., Fortuna, L., Manganaro, G. [1995] "Chua's circuit can be generated by CNN cells," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.2, pp.123-125.
·          Arena, P., Baglio, S., Fortuna, L., Manganaro, G. [1995] "Simplified scheme for realisation of Chua oscillator by using SC-CNN cells," Electronics Letters, vol.31, no.21, pp.1794-1795.
·          Arena, P., Baglio, S., Fortuna, L., Xibilia, M.G. [1995] "Chaotic time series prediction via quaternionic multilayer perceptrons," 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century (Cat. No.95CH3576-7). IEEE. Part vol.2, pp.1790-1794.
·          Arena, P., Caponetto, R., Fortuna, L., Muscato, G., Xibilia, M.G. [1996] "Quaternionic multilayer perceptrons for chaotic time series prediction," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E79-A, no.10, pp.1682-1688.
·          Arena, P., Fortuna, L., Porto, D., Rizzo, A. [1999] "Self-organisation in arrays of nonlinear systems induced by chaotic perturbation: An experimental approach," ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349). IEEE. Part vol.5, pp.479-482.
·          Astakhov, V., Shabunin, A., Anishchenko, V. [1998] "Synchronization of self-oscillations by parametric excitation," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.7, pp.1605-1612.
·          Bartissol, P., Chua, L.O. [1988] "The Double Hook (Nonlinear Chaotic Circuits)," IEEE Transactions on Circuits & Systems, vol.35, no.12, pp.1512-1522.
·          Bernardo, M.Di [1996] "A purely adaptive controller to synchronize and control chaotic systems," Physics Letters A, vol.214, no.3-4, 13 May 1996, pp.139-144.
·          Berns, D.W., Moiola, J.L., Guanrong, C. [1998] "Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.45, no.7, pp.759-763.
·          Berns, D.W., Moiola, J.L., Guanrong, C. [1998] "Predicting period-doubling bifurcations in nonlinear time-delayed feedback systems," Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187). IEEE. Part vol.3, pp.619-622.
·          Biey, M., Bonani, F., Gilli, M., Maio, I. [1996] "Influence of the parasitics on the time delayed Chua's circuit," 8th Mediterranean Electrotechnical Conference. Industrial Applications in Power Systems, Computer Science and Telecommunications. Proceedings (Cat. No.96CH35884). IEEE. Part vol.1, pp.443-446.
·          Biey, M., Bonani, F., Gilli, M., Maio, I. [1997] "Qualitative Analysis of the Dynamics of the Time-delayed Chua's Circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.44, no.6, pp.486-500.
·          Biey, M., Gilli, M., Maio, I., Premoli, A. [1998] "A computer program for accurate time-domain analysis of 1D-arrays of Chua's oscillators," Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187). IEEE. Part vol.3, pp.383-386.
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