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Some examples of such failures in risk assessment include the use of Gaussian models in finance Black—Scholes , the Gaussian copula , LTCM , the use of Gaussian processes and linear wave theory failing to predict the occurrence of rogue waves , the failure of economic models in general to predict the financial crisis of — , and the under-appreciation of external events, cascades, and nonlinear effects in probabilistic risk assessment , leading to not anticipating the Fukushima Daiichi nuclear disaster in Such high impact failures emphasize the importance of the study of extremes.

The dragon king concept raises many questions about how one can deal with risk. Of course, if possible, one should avoid exposure to large risks often referred to as the black swan approach.

However, in many developments, exposure to risk is a necessity, and a trade-off between risk and return needs to be navigated.

This nontrivial case is the one that must be considered. In an adaptive system, where prediction of dragon kings is successful, one can act to defend the system or even profit.

How to design such resilient systems , as well as their real time risk monitoring systems, [39] is an important and interdisciplinary problem where dragon kings must be considered.

On another note, when it comes to the quantification of risk in a given system whether it be a bank, an insurance company, a dike, a bridge, or a socio-economic system , risk needs to be accounted for over a period, such as annually.

Typically one is interested in statistics such as the annual probability of loss or damage in excess of some value value at risk , other tail risk measures , and return periods.

To provide such risk characterizations, the dynamic dragon kings must be reasoned about in terms of annual frequency and severity statistics.

These frequency and severity statistics can then be brought together in a model such as a compound Poisson process. If not, one may only construct scenarios.

However, in any case, given the uncertainty present, a range of scenarios should be considered. Due to the shortage of data for extreme events, the principle of parsimony , and theoretical results from extreme value theory about universal tail models, one typically relies on a generalized Pareto distribution GPD tail model.

However such a model excludes DK. Thus, when one has sufficient reason to believe that DK are present, or if one simply wants to consider a scenario, one may e.

From Wikipedia, the free encyclopedia. Redirected from Dragon King Theory. Event that is both extremely large in impact and of unique origins.

Sornette, Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth, Proc.

Extreme events in nature and society. A simple test for deviations from the power law". Carlson , and James S.

B1 : — Bibcode : PhyA.. Miltenberger, and C. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering.

Anifrani, C. Le Floc'h, D. Sornette and B. Souillard, Universal Log-periodic correction to renormalization group scaling for rupture stress prediction from acoustic emissions, J.

I France 5 6 : — Spontaneous generation of discrete scale invariance in growth models. Physical Review E, 55 6 , Johansen and D.

Sornette, Critical ruptures, Eur. B 18 : — Sammis and D. Springer Berlin Heidelberg, Below, and Ph Hoyois. Louvain, Brussels: Belgium.

Categories : Prediction Dynamical systems Risk management Statistical outliers Black swans Metaphors referring to animals. Hidden categories: Articles with short description.

Namespaces Article Talk. This retro television episode is one that will stick with you, make you uncomfortable, but yet enjoyable.

Another supernatural entity first appeared in the pages of Marvel Comics back in the s alongside Ghost Rider- the Son of Satan!

Damian Hellstrom I nice devilish name has occasionally appeared ever since in the pages of his own comic book series and as a member of The Defenders.

In our current series we are examining the stories we tell that help us deal with the unknown and this story- the Son of Satan, not only deals with devils and demons but with our on family issues as well.

Even your dad wasn't this bad. Join Karl Stern as he discusses the Son of Satan. We continue our look at supernatural aspects as presented in comic book stories and this week we visit the theme of avenging angels!

These are angelic beings sent by a high power to right wrongs and serve justice. Obviously, these beings are vastly powerful and are based on archetype biblical angels.

The Specter, Angela, and other powerful beings sent to serve justice are explored in this episode of DragonKing Dark. We begin a new series at DragonKing Dark this week.

For a few weeks we will be looking at comic book character with supernatural stories. For several weeks now we have been exploring our fascination with the unknown, the paranormal, and the super natural through the stories we tell.

After examining several movie characters we now want to shift our focus to another area of retro pop culture where many movie characters are mined from: comic books.

The first character we look at is the Marvel Comics character Ghost Rider who rode onto comic book pages in the s and continues to this day.

He had two movies and is one of the best character designs in comic book history. The Joker debuted in Batman issue 1 way back in and has been interpreted many ways, both in the comics and in movies.

Cesar Romero's slapstick Joker, Jack Nicholson's strange comic bookie Joker, Heath Ledger's award winning drug-addled inspired Joker, Jared Leto's new punk version, and Joaquin Phoenix's brilliant exploration of mental illness.

We continue our look at complex movie villains with a dark or supernatural aspect to them. Upon first viewing in , No Country For Old Men became one of my favorite movies and much of that surrounded how I related to Tommy Lee Jone's Ed Tom character but even more to Javier Bardem's Anton Chigurh who is both a great straight up bad guy, but beyond that, a psychological analog to the never-ending presence of evil in the world.

This week, host Karl Stern takes a look at another movie villain who is more than a one dimensional brute. We travel back to, what many feel, was the worst of the Nolan Batman films, however, the lead antagonist is an extremely interesting character.

Bane is, on first examination, a brute. A strongman who aims to "break the Bat" as per comic book lore. However, there is much more to Bane than meets the eye This week on DragonKing Dark, we explore the story and psychology of another icon of fear and horror - Jason Voorhees from the Friday the 13th movie series.

The story of Jason changed frequently throughout the movie franchise but the stalking element of fear and surprise remained constant.

DragonKing Dark continues to explore elements of the supernatural, fear, and paranormal through the stories we tell and this week we look back at one of the most iconic film series ever.

Here he is, Humungus, the Lord Humungus. The master of the wastelands. The Ayatollah of rock and rolla! As we live through this pandemic we are going to look at some pop culture that tells us stories of how the future could be.

On this edition of DragonKing Dark, host Karl Stern journeys back in time to for an episode of the sci-fi fueled TV show the Outer Limits and an episode titled The Solider which may have influenced The Terminator series of movies.

A solider from the future is accidentally beamed back in time and tries to mesh with the world of and the results are less than successful.

Of all the ancient monuments in Giza complex in Egypt, one stands out as different from the others. The great Sphinx seems out of place, out of scale, and older than the rest.

The official archaeological story says different but one can see with their own eyes that the head is out of scale to the body and there are clear signs of water erosion.

What's up with that? We discuss the age and theories of The Sphinx. The Venus death probe was indestructible, built to withstand the harsh conditions of the planet Venus.

Then we will look at the reality behind the Venus probe including Russia's actual successful landing of a probe on Venus, the only pictures from it's nightmarish surface, and some really cool information about the hell world that is Venus.

This episode takes a look at a haunted house one of my favorite topics , a haunted car and other haunted objects, and much more.

We venture into the realm of ghosts and demonic activity. One of the most popular pop culture monsters of the s was the Loch Ness monster, a supposed displaced dinosaur or sea creature in a deep Scottish lake.

Nessy even made it into a song by The Police and Napoleon Dynamite. While the Loch Ness monster also seems like a plausible real thing that could exist, it turns out, it's the most likely of the famous s monsters not to be real.

This documentary from takes a look at how the Loch Ness monster turned out to be nothing more than a plot to get revenge on a newspaper.

Not only does Bigfoot arrive but he's has bionic enhancements as well. Bigfoot is played by both pro wrestler Andre the Giant and Ted Cassidy.

We talk about Bigfoot hysteria in the s and how pop culture treated Bigfoot. We will look back at the facts and fiction of tying the real-life Vlad Tepes to the fictional vampire lord Dracula.

While Bram Stoker's Dracula gets his name and much of his home setting from Vlad the Impaler, there is some question of how much the two Dracula's have in common.

We take a look back at this documentary and discuss what has changed since then. This week on DragonKing Dark, Karl takes a look at a documentary from about the cult s supernatural themed soap opera Dark Shadows.

We have talked about Dark Shadows before at When It Was Cool and this documentary promised a look behind the scenes and at the creator of the series- Dan Curtis.

While it fell short in that area, it excelled in taking a look at the most interesting character from the show- Barnabas Collins.

Patreons get an ad free version of the show. The Yeti is a creature similar to Bigfoot in many respects, only in colder climates.

But what evidence of the Yeti do we actually have? Do we have more or less than Bigfoot? There is even some claimed evidence of the existence of the Abominable Snowman in the form of a mummified hand and scalp.

How well do these hold up to examination? Find out this week on DragonKing Dark. Our retro TV review this week goes back into the In Search of In this episode, Leonard Nimoy navigates us through the usual Bigfoot stories- men trapped in a cabin under siege from a group of creatures, obviously the Patterson film story, and many other close encounters with a giant ape-man in the Pacific Northwest.

If you're a Bigfoot enthusiast then this show was produced during the height of the s Bigfoot-mania. We all know the name as one of the greatest directors and minds of the last years.

Orson Wells narrates this amazing documentary Future Shock based on a book by the same name.

Unlike so many other futurism documentaries and books, this one gets it right. In fact, frighteningly so. No flying cars or homes of the future here.

Instead, it seems a society shocked into depression over the rapid advancement in technology. With 50 years of perspective since Future Shock aired, it actually seems more relevant than ever.

This is a documentary that is an explosive expose on UFOs and what the government, not just in the United States but the UK as well, know.

Interviews with very credible insiders leave little doubt that UFOs have been here, are currently here, and it is known inside the halls of power.

An excellent documentary on UFOs. We change course here to bring things more in line with the other shows at WhenItWasCool. This week, host Karl Stern takes a look at two shows.

First, from the old series In Search Of Then the second half of the show looks at episode 1 of the Pyramid Code which dives into the mysteries of the Egyptian Pyramids!

This is a great jumping-on point for this podcast! Come join us! This week we travel to the Great Lake state of Michigan to find dinosaurs, museums, and a few oversized objects of interest.

Spread the word about DragonKing Dark and let's have a few giant sized weeks of our own! We take a look at one of the oldest states in the Union and try to find the strangest, most odd, and unusual places.

Massachusetts has the usual stuff like oddity museums, and largest something-or-other but they also have a history of witch hunts and a township that is probably the most associated with witchcraft on Earth.

Join host Karl Stern as he explores the oddities of Massachusetts. I had the privilege of going to Maryland a couple of years ago and really enjoyed it.

In this episode we take a look at odd graves, strange museums, and macabre stories. Come join us with a look at the strangle places in Maryland.

Obviously, the home of Stephen King is one of them but Maine is old state and, along the way, has amassed a collection of ghosts, witches, and strangeness all it's own.

Let's head northeast and see what oddities Maine has to offer. When you think of strange, odd, and weird places, Louisiana probably comes to mind because of New Orleans and it's association with Voodoo and Vampires.

They also apparently believe that Louisiana is made up entirely of New Orleans and this drives host Karl Stern crazy. We stop this week in Kentucky, this nice mid-south state is well known for horse racing but also offers up many strange and unusual attractions including one of the most well known and controversial tourist attractions in America - the Creationist museum built inside a full size replica of Noah's ark.

Join us on our look at the oddities of Kentucky. Home to Dorothy of the Wizard of Oz. What oddities can we find here? As it turns out, quite a few.

Kansas likes it's stuff big as there are a lot of the largest things in the world on display throughout the state. There is also even a museum of the smallest version of the largest things!

This episode we make a stop in Iowa and what could Iowa possibly have to offer? You'll be surprised! Iowa, as it turns out, is packed with lots oddities including the fictional birthplace in the future of Captain Kirk and is home to several of the largest objects in the world!

Come join us for a trip into the unusual that Iowa has to offer. What bizarre stops and attractions would Indiana possibly have to offer?

Come with us as we check out ruins, lot's of giant stuff, murders, and mysteries with oddities of Indiana! Then, as we will all discover, Illinois actually prides itself on the strange and unusual!

From giant rocketmen to giant rockmen and all sorts of weird stuff in between, join DragonKingKarl as he explores the land of Lincoln to find the strangest stuff there!

Searching for old family members, the history of our town, and more. Reading newspapers from the s through the s over and over again makes you realize that we aren't so special here in In fact, the more that things change, the more they stay the same.

You can add radio, television, go to the moon, have multiple wars, the internet, and every political argument you can think of but in the end human nature seems consistent.

It's true crime meets Halloween with stories from the early s when, apparently, Halloween could get pretty rough.

From the streets of Chicago to rural America, Halloween has seen it's share of killings. From the WhenItWasCool.

You know I advise against it but in this instance there has been a lot of talk about UFOs and aliens recently. Are we being prepped for an announcement of alien life in the near future?

These songs are especially chosen for those fans of paranormal and horror type shows and includes music recommendations by people like Black Sabbath, Ozzy Osbourne, Dio, and more!

It's music to make give you chills on this edition of DragonKing Dark. This show was so popular that it spawned multiple follow-ups.

Host Karl Stern takes a look at some colorful and bizarre obituaries from the Victorian age of newspapers into the early s.

Back then, newspapers didn't mind at all giving you all the gory details about the Angel of Death visiting the neighbor down the street.

Yes, they even tout their famous potatoes on their car tags but I was pleasantly surprised they have quite a few interesting oddities, roadside attractions, and weird places too.

Come on a road trip with Karl Stern to visit Idaho and the strange stops in this rural state! We are at war. You might not think so but we are.

American society is being manipulate and shots both literal and figurative have already been fired. Don't be duped into believing what you see on the news is something it's not.

We often talk about unfounded fears but the fears this time may be well founded. This week we talk about monsters but not the kind you might be expecting.

He looks at some of the more strange, odd, and weird places in this tropical paradise which is rich with history and the ancient wisdom and traditions of the people who live there.

We discuss various stories about people who have claimed to have had similar experiences as their bodies approached clinical death.

What happens to the soul once we die? Is there even a soul? Here is Your Super Power asks the question, if you were given a comic book super power what would you actually do with it?

We examine several comic book characters who either use their powers for good or evil and ask ourselves what would really happen in a real world setting?

You probably know that Florida has a reputation for being a bit strange. Florida is a neighboring state to me and my wife if from there so we have a lot of Florida experience.

This week on DragonKing Dark we discuss the oddities and unusual places in this often most unusual state of Florida!

Plus, your usual assortment of UFOs and other beyond the norm stories. A state that host Karl Stern has only been to once - Delaware!

This small state is nestled with the Atlantic Ocean on one side and Washington DC on the other so there must be some weird stuff there right?

Our Patreons get an ad free version with bonus content. Stay tuned! Are there any that actually pass the slightest bit of inspection and make you go, "hmmm?

Will you be brave enough to break the seal on this episode? Patreons get an ad free version of the show with bonus content.

Witch Hunt and The Weapon both have overtones of religion, oppression, and darkness. One of our early shows was titled Music for the Mind and this is an extension of that.

This week I give you an episode of our Patreon exclusive series DragonKing Darker where I visited more crazy bullshido stories with tales of the Din Mak death touch, pressure points, and more!

Grab your Nunchucks and let's get kicking! It is a hotbed of paranormal spots due, in part, to the Warren family of The Conjuring fame.

This week on DragonKing Dark, host Karl Stern takes a deeper dive into the list to pick out the movies which have more of a horror or occult theme to them.

DragonKing Dark is your weekly dose of the strange, bizarre, odd, and unusual. Patreons get an ad free extended version of the show and this week we take a look at recent comments and questions from our Patreons.

We love Colorado and have been there a few times and have even seen a few of these ourselves. This episode even solves the mystery of a road sign we've wondered about since the first time we saw it.

Visit the more unusual places in Colorado with this edition of DragonKing Dark. A young star dies of an unexpected health emergency, another is murdered, and others still befall a series of bizarre calamities.

Arkansas is a beautiful state filled with flat farmland, plentiful forests, and the scenic Ozark mountains.

It is also oddly home to a lot of weird stuff. Patreons you get a special riding around with Karl after-dark bonus feature. Tragedy and misfortune has been linked to appearing as the iconic DC Comics character.

From the strange and controversial death of George Reeves to the tragic injury and ultimate death of Christopher Reeve many associated with the role of Superman have met with trouble.

Is Superman a career killer for an actor? How many others have met with tragedy while associated with Superman? Karl from WhenItWasCool.

Patreons get an ad free extended version of the show. A variety of dark themed topics pepper the news over the last few weeks mostly dealing with strange and amazing aspects of science.

On this episode we journey from the depths of the sea to the outer reaches of space to find out that reality is sometimes stranger than fantasy.

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Chicken Lo Mein. Shrimp Lo Mein. Beef Lo Mein. Related religions. Main article: Yellow Dragon. Main articles: Azure Dragon and Ao Guang.

Main article: Ao Run. Dragon King sculpture with residual traces of pigment, dated 11th—12th century, Japan.

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Help Community portal Recent changes Upload file. Wikimedia Commons. The theory of black swans is epistemological , relating to the limited knowledge and understanding of the observer.

The term was introduced and popularized by Nassim Taleb and has been associated with concepts such as heavy tails , non-linear payoffs, model error, and even Knightian uncertainty , whose "unknowable unknown" event terminology was popularized by former United States Secretary of Defense Donald Rumsfeld.

Taleb claims that black swan events are not predictable, and in practice, the theory encourages one to "prepare rather than predict", and limit one's exposure to extreme fluctuations.

The black swan concept is important and poses a valid criticism of people, firms, and societies that are irresponsible in the sense that they are overly confident in their ability to anticipate and manage risk.

However, claiming that extreme events are—in general—unpredictable may also lead to a lack of accountability in risk management roles.

In fact, it is known that in a wide range of physical systems that extreme events are predictable to some degree.

This is the domain of the dragon kings. Such events have been referred to as Grey Swans by Taleb. A more rigorous distinction between black swans, grey swans, and dragon kings is difficult as black swans are not precisely defined in physical and mathematical terms.

However technical elaboration of concepts in the Black Swan book are elaborated in the Silent Risk document.

An analysis of the precise definition of a black swan in a risk management context was written by Prof. Terje Aven.

It is well known that many phenomena in both the natural and social sciences have power law statistics Pareto distribution.

The result of this is that, when dealing with crises and extremes, power law tails are the "normal" case.

This property implies that all events—both large and small—are generated by the same mechanism, and thus there will be no distinct precursors by which the largest events may be predicted.

A well known conceptual framework for events of this type is self-organized criticality. Such concepts are compatible with the theory of the black swan.

However Taleb has also stated that considering the power law as a model instead of a model with lighter tails e.

In a variety of studies it has been found that, despite the fact that a power law models the tail of the empirical distribution well, the largest events are significantly outlying i.

Examples of this include the largest radiation release events occurring in nuclear power plant accidents, the largest city agglomeration within the sample of cities in a country, the largest crashes in financial markets, and intraday wholesale electricity prices.

Physically speaking, dragon kings may be associated with the regime changes, bifurcations , and tipping points of complex out-of-equilibrium systems.

However, it is well known that in dynamic systems, there are many precursors as the system approaches the catastrophe.

Positive feedback is also a mechanism that can spawn dragon kings. For instance, in a stampede the number of cattle running increases the level of panic which causes more cattle to run, and so on.

In human dynamics such herding and mob behavior has also been observed in crowds, stock markets, and so on see herd behavior.

Dragon kings are also caused by attractor bubbling in coupled oscillator systems. These excursions form the dragon kings, as illustrated in the figure.

It is claimed that such models can describe many real phenomena such as earthquakes, brain activity, etc. It could also be the case that dragon kings are created as a result of system control or intervention.

That is, trying to suppress the release of stress or death in dynamic complex systems may lead to an accumulation of stress or a maturation towards instability.

Such fires are inconvenient and thus we may wish that they are diligently extinguished. This leads to long periods without inconvenient fires, however, in the absence of fires, dead wood accumulates.

Once this accumulation reaches a critical point, and a fire starts, the fire becomes so large that it cannot be controlled—a singular event that could be considered to be a dragon king.

Other policies, such as doing nothing allowing for small fires to occur naturally , or performing strategic controlled burning , would avoid enormous fires by allowing for frequent small ones.

Another example is monetary policy. Quantitative easing programs and low interest rate policies are common, with the intention of avoiding recessions, promoting growth, etc.

However, such programs build instability by increasing income inequality, keeping weak firms alive, and inflating asset bubbles.

DK are outliers by definition. However, when calling DK outliers there is an important proviso: In standard statistics outliers are typically erroneous values and are discarded, or statistical methods are chosen that are somehow insensitive to outliers.

Contrarily, DK are outliers that are highly informative, and should be the focus of much statistical attention.

Thus a first step is identifying DK in historical data. Existing tests are either based on the asymptotic properties of the empirical distribution function EDF [13] or on an assumption about the underlying cumulative distribution function CDF of the data.

It turns out that testing for outliers relative to an exponential distribution is very general.

The latter follows from the Pickands—Balkema—de Haan theorem of extreme value theory which states that a wide range of distributions asymptotically above high thresholds have exponential or power law tails.

As an aside, this is one explanation why power law tails are so common when studying extremes.

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