Self-Organized Criticality
We’ve all heard about the “Straw that broke the Camel’s back.” Indeed every extra weight wears on the back support of the camel's spine until the burden is too much and the ligaments rupture, the muscles fray, bones fracture and the sinews give out. The cascade is not a sudden departure but a slow progressive instability that ensues leading to the catastrophic failure.When sorrows come, they come not single spies, but in battalions ~Shakespeare -Hamlet (Act IV, Scene V)
Sand-Pile Self-Organized-Criticality
To articulate it better, let us look at an avalanche, you know one of those 180 miles per hour gigantic clouds of ice and snow running down the mountainside, demolishing all the trees and structures in its path? Yes that one. Well it turns out that there are progressive “fingers of instability” present there too.
The compressed ice over the previous layer of snow/ice via the power of thermodynamics liquefies the boundary layer. The snow layers above slip and slide and start the avalanche.
It can manifest as a snow, slab or water flow state depending on frigidity of the moisture.
A similar phenomenon is implicated in the pyroplastic nightmare of a volcanic lava flow and the geological weakened anchors in land-slides; the latter is a progressive system of instability that allows small pebbles to create the sliding mechanism leading to years of uninhabitable space.
The Bak-Tang-Weisenfel Sand pile Model reiterates the meaning of a progressive building instability and the cataclysm that follows with “one more grain of sand.” This is termed as a Self-Organized Criticality.
The Sand Pile Experiment essentially determines that critical juncture of stability vs. instability. As the sand is piled on the surface and the slope builds up, the grains of sand are poured onto the pile, one by one, until the slope exceeds a specific threshold value and the site collapses transferring sand into the adjacent sites, increasing their slope. During the build-up of the sand-pile there are small unstable elements within the pile. As more and more unstable elements form, a critical threshold once transgressed leads to the collapse.
Genes and Mutations
The Knudsen One-Two Hit Hypothesis in Heritable and Non-Heritable Cancers
Changing gears and reflecting about the human body one finds the same fingers of instability present. Ever hear about a Knudsen’s Hypothesis. Well, the hypothesis states that since there are two alleles of each gene one on each arm of the chromosome, therefore it takes two hits in sequential order or concurrently to dislodge a gene function via mutation. One allele mutation weakens the gene but does not alter the function. However loss of both alleles disrupts that gene's function. If the targeted gene is a tumor suppressor gene then that suppression will be circumvented and any (promoter) oncogene can have a field day in initiating and promoting cancer. A case in point is the BRCA1 gene that is a tumor suppressor gene. Its normal functioning protects against malignant transformation of cells in various organs. A mutated/damaged BRCA1 gene leads to a propensity for breast, ovarian, colon and prostate cancers, to name a few. Its like granny driving a red Ferrari with one foot on the brake pedal and other on the accelerator, easing on the brakes, look out! So if those tiny fingers of instability exist as a loss/damage of one allele during birth or via inheritance, followed by a second blow from an external source such as consumed chemicals or exposure to radiation fields etc. then the cancer cascade begins.
Multi-lineage Hits on the Retinoblastoma Gene
The Linear Logic of Colon Cancer Genetic Mutation
Taking the theme further, let us look at the phenomenon of Colon Cancer. Here the initial “finger “ is the APC gene mutation. Again the gene carries two alleles and each of them has to be knocked out to start the process of initiating a polyp in the colon. This gene then governs the initial process, failing APC mutation the process does not move ahead. In other words if the APC gene mutation is prevented then colon cancer may not form or even propagate. Aspirin and NSAIDs seem to work through the COX-2 mechanism that shuts down the polyp formation. In fact current data suggests a 60% reduction of colon cancer in people taking Aspirin or NSAIDs. It remains unknown whether the mutated gene is dysregulated or whether it’s effect is marginalized by Aspirin. So, here we have the first finger of instability in relation to the colon malignancy. We now add to that another gene called DCC gene that allows the polyp to grow bigger. There are cases and gastroenterologists will share this with you, that they have seen; large poypoidal non/pre-cancerous growths obstructing the colon but these growths never converted to cancer. There, is the non-random linear stream of genetically mutated continuity that drives the malignant process. In other words, if the next sequence of genetic events in the polyp’s history does not take place, the transformation into cancer is arrested. Moving on, now lets add the p53 gene mutation into the mix and voila, the “avalanche” starts and cancer begins. The last step in this unholy process is the H-Ras gene. Add this into the cauldron of this “Hubble, Bubble, Boil and Trouble” witches brew and now the fully formed colon cancer acquires the ability to spread across many planes, in other words metastasize. So as it is abundantly clear, the fingers of instability exist in the genome and each change adds to the certainty of the outcome but not the time.
Wild-Type Gene Insertions
I might be taking a less traveled path here, but the fingers are going and if you have the patience to read, come along for the ride. Picturing the dynamics of this eventuality one finds the system can be arrested at various levels of the growth phase. Aspirin as I mentioned has been shown in many studies to prevent polyp formation- the precursor to the colon cancer, and equally, adding a “Wild-Type” (Wild-Type means a fully functional unmutated form of the natural gene product) DCC gene or a fully functional “wild-type” p53, where a mutated p53 exists, might also arrest the course of the disease. In fact studies have been done in prostate cancer where “wild-Type” p53 gene infused via viral vectors, resulted in abrogation of a rapid growth phase in the prostate cancer cells. Food for thought and further research!
Malignant Lymphoma
Let me take you into another scenario that was developed back in the 1970s by two US pathologists R.J. Lukes and L.D. Collins who devised a classification of Non Hodgkins Lymphoma based on immune nature of the lymphocytic cell line (Lymphomas arise from the white cells called lymphocytes and these cells are responsible for humoral and cellular immunity in the body). This was a tedious task that won over many hearts. In fact at the core of the classification was the premise that cell growth arrests at various stages of growth of a lymphocytic cell leading to an over abundance of the arrested cell population that leads to malignant Lymphoma. The earlier the phase-arrest occurs, the greater the chance of a more aggressive Lymphoma and the later the blocked growth, the more timid the disease with a slower biological growth rate and a longer life span for the individual so afflicted. The classification was based on the morphological views of the cell. The fingers of instability in the Lymphoma are like the “arresting cables,” that are genetically determined. These mutations it is believed can occur from many determined and indeterminate environmental sources such as fertilizers and benzoate compounds. So as the genes play out their drama ( in this case the BCL2, or via Chromosomal translocations like 11:14 etc.), the time of arrested development determines the viciousness of the disease.
Chromosome 11:14 Translocation in Lymphoma
Life, therefore is lived with these fingers of instability. We are always teetering on the edge of survival. Science estimates that about 10,000 hits occurring on our DNA is a daily affair. It is the built-in mechanism of safety with the DNA-Mismatch repair mechanism that keeps us embroiled in the dynamics of living. Failing this mechanism the DNA takes a hit at a single nucleotide or multiple nucleotide levels and that leads to a change and the Mismatch repair mechanism unable or overwhelmed by the suddenness leads to a formative DNA change and causes unholy hell. The plot thickens, the pulse races, be still my heart.
Rhythms of the Heart
Sino-Atrial and A-V Node
Speaking of the heart, now here is a crafty four chamber hollow organ that evolves from a tube and continues it's rhythmic beat for 3 billion times in a 80 year old life span. Match that to a Chevy, Benz or Lamborghini or for that matter even the Ford Model A and the simple answer is "No maas." In that history of time the heart suffers so many whips and scorns and as many winks and smiles that the accumulated physical and emotional stress takes it's toll. From the sludge of the excess food deposits, the trauma of the minor inflammations and compromised blood supply to the organ, the constant A-V Node that synchronizes the pulse and rhythm of the heart may with deprived nourishment, abrogate it's authority to other competing minor neural node stakeholders in the atria or the ventricles.
Thus the drama of irregular heart rhythm begins. Since the quivering organ does not carry the same "push" to disperse the blood through hundreds of miles of capillaries, "heart failure results. Each extra grain of insult added to the pile of time ultimately collapses the synchronicity of the A-V Node and that sudden departure from rhythm takes a life. The Self-Organized Criticality finds a new victim, proceeding from the ignorance in innocence, through ignorance of change to a loss of human life. Not only the rhythm but the damaged muscle function can bleed strength away, leading to the euphemistic term "Cardiomyopathy." Whatever the ultimate pathology that grates this organ is, the ultimate race is towards a congested heart state leading to heart failure.
Aviation
Aloha Airline Decompression and Metal Fatigue
Disparate groupings of animate and inanimate issues show the relevance of this Instability concept in other walks of life. I will take you to another realm called aviation. Airplanes fly, we know that, you can drive them on the roads too if you prefer, but at greater fuel costs and traffic tickets. They (the airplanes) too are subject to these invisible but certainly palpable “fingers of instabilities.” Let me explain further. Remember Aloha Airlines in the 1990s with the fuselage ripped off from the multiple compression/decompression phases of pressurization from thousands of flights, as it landed in Alaska and presented an awesome photo opportunity with passengers alive and seat-belted in their seats. What happened there was metal fatigue.
US Airways Skin Rupture
A similar event happened to a US Airways airplane recently when a 3-foot piece of aluminum plate was blown off just in front of the rear vertical empennage. No injuries were reported, except rapid decompression. Metal fatigue at vulnerable joined surfaces was blamed. This of course led to a NTSB and FAA requirement for annual survey of the weak points in all commercial aircraft. Early discovery of fracture lines leads to proactive replacement of the piece in qiestion. The instability is thus checked. Damage contained.
Economic Fingers of Instability and the Crash
And one last bastion of instability, to no one’s surprise is the Economy. Add to the normal barter system of, “I have what you need, but it will cost you…” the dynamics of leveraged arbitrage where the buyer does not know the seller and the seller who bought it from some one else at a lower price, does not know the initial product seller. This is the very crux of the CDS debacle that usurped trillions of dollars in equity around the world. The smarty-pants, mathematically oriented “Quants” added one Ponzi scheme atop another and the fingers of instability lost traction. The net result is a world in chaos. While the blame game continues and the finger pointing gets more intense with the passage of each day as the financial system contracts from its mythical rarified peaks, the regression to the mean follows that will level the field for all, over time. The high-flyers will trim their assets as will everyone else. Thus with such extravagance of hi-falutin words rendered as evidence from economists and deeds by their minions, instability is created and when it does exceed the threshold, please remember when you hear this, “It can’t happen.” means, it will! As Benjamin Zhang explains in his article referenced below; “Moreover, the marginal impacts of volatility and jump measures increase dramatically from investment grade to high-yield entities.” Meaning the higher the yields (return) the greater the risk on the opposite side: loss, for instance! He further goes on to state, “Historical skewness is an indicator of asymmetry in asset returns. A large and positive skewness means that extreme upward movements are more likely to occur. Nevertheless, skewness is not a sufficient indicator of jumps. For example, if upward and downward jumps are equally likely to occur, then skewness is always zero. However, jump volatility RV(J) and kurtosis are direct indicators of the existence of jumps in the continuous-time framework, but the fact that both measures are non-negative suggests that they are unable to reflect the direction of jumps, (my emphasis) which is crucial in determining the pricing impact of jumps on CDS spreads.” Meaning that the Jumps occur on both sides of the coin, High net returns and high net losses. Try trillions of dollars of loss since the 2007-2008 window period and counting. The United States financial system has faced many downturns, a total of 21 Recession, the current one being the 22nd since 1900. What is interesting is that of the 21, only two others have been this deep. The other two were The Great Depressions of 1921-1922 and 1929-1933. The Self-Organized Criticality also suggests that there are many more fingers of instability in smaller sand-piles then there are in larger ones. Smaller sand-pile breakdowns are easily recovered from, yet the smaller ones if they remain organized and stable, can temporarily withstand the critical factor of breakdown towards a larger window of time until the combined criticality is reached in the larger sand-pile, a power-law distribution related chain reaction occurs and the back of the banks really breaks!
Moderation
So what do we learn from this: Moderation. Moderation is tolerated for a much longer time in life and living, then is excess. Building taller castles real and or imagined have more fingers of instability automatically included in their structure. Surprised at that? You shouldn’t be, if you had followed the logic. The larger the structure created, the more spectacular the fall. Remember Bernie Madoff? Anyway, history is replete with examples but we humans beings constant in our habits, categorize events, itemize them and cubby-hole them for posterity in minimalistic fashion. Never do we relate them to each other and to others for grasping the essence of the universal truth. What the Self-Organized Criticality shows us that a small wave is easily deflected while a tsunami has gross devastation written all over it. A single economic system collapse is weathered easily but subjecting the entire world to a global single unitary system of economics and culture is tantamount to annihilation. Similarly a single mutation in an individual can lead to an unfortunate loss of one life but modulating the genome of a large populace is looking for unmitigated disaster ~extinction.
The Cosmic Rip
References:
Per Bak, Chao Tang and Kurt Wiesenfeld (1987). "Self-organized criticality: an explanation of 1/ƒ noise". Physical Review Letters 59 (4): 381–384.
Naoto Yoshioka . A sandpile experiment and its implications for self organized criticality and characteristic earthquake Earth Planets Space, 55, 283–289, 2003
http://www.bis.org/publ/
http://www.thelancet.com/
http://www.nature.com/scitable/topicpage/Tumor-Suppressor-TS-Genes-and-the-Two-887
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