BSC 417/517

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Lecture 3

• BSC 417/517
• Environmental modeling

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FEEDBACK!

• A feedback loop in a dynamic system can be
  defined as a closed-loop circle of cause and
  effect
• Conditions in one part of the system cause
  results elsewhere in the system, which in turn
  influence conditions
• Learn to identify these in models by their
  spatial relationship

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Feedback

• Definition Feedback is a process whereby some
  proportion of the output signal of a system is
  passed (fed back) to the input. This is often
  used to control the dynamic behavior of the
  system

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The ideal feedback loop in non-Stella iconography
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Positive and negative

• Types of feedback are
• Negative feedback which tends to reduce output
  (but in amplifiers, stabilizes and linearizes
  operation)
• Positive feedback which tends to increase
  output or
• Bipolar feedback which can either increase or
  decrease output

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First, a bit on the history of feedback

• Negative feedback was applied by Harold Stephen
  Black to electrical amplifiers in 1927
• In 1921,  Black joined the forerunner of Bell
  Labs, in New York City, working on elimination of
  distortion
• After six years, Black invented the negative
  feedback amplifier commuting to work aboard the
  ferry
• Basically, the concept involved feeding systems
  output back to the input as a method of system
  control
• The principle has found widespread applications
  in electronics, including industrial, military,
  and consumer electronics, weaponry, analog
  computers, and such biomechanical devices as
  pacemakers
• Forerunner thermostats, railroad engines

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History of feedback cybernetics

• Norbert Wiener
• Formalized the notation and scientific process of
  feedback as communication and control within
  systems, including computer, human, and animal
  systems
• The foundation of computing and various modern
  sciences
• Systems biology
• Ecology
• Process optimization
• Environmental modeling

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Ol Norbert
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History of feedback cybernetics

• Forerunner of Norbert Wiener Arturo Rosenblueth
• A Mexican researcher and physician whose 1943
  paper Behavior, Purpose and Teleology, proposed
  that behavior controlled by negative feedback,
  applied to either animal, human or machine was a
  fundamental principle of systems

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Norbert Wiener your bedtime reading

• 1948, Cybernetics Or the Control and
  Communication in the Animal and the Machine.
  Cambridge, MA MIT Press.
• 1950, The Human Use of Human Beings. Da Capo
  Press.
• 1966, Nonlinear Problems in Random Theory. MIT
  Press.
• 1966, Generalized Harmonic Analysis and Tauberian
  Theorems. MIT Press.
• 1966, God Golem, Inc. A Comment on Certain
  Points Where Cybernetics Impinges on Religion.
  MIT Press.
• 1988, The Fourier Integral and Certain of its
  Applications (Cambridge Mathematical Library).
  Cambridge Univ. Press.
• 1994, Invention The Care and Feeding of Ideas.
  MIT Press.

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Positive feedback

• An amplifying system
• A system that responds to perturbation in the
  same direction as the perturbation
• May lead to unstable equilibrium and explosive
  conditions
• Acceleration of effects leading to big changes

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Examples

• The familiar audio screech in the positive loop
  between microphone and amplifier
• Increasing temperatures leading to melting of the
  ice caps leading to reduced reflection of the
  suns rays leading to further warming
• The hyperbolic growth of the world population
  observed till the 1970s has recently been
  correlated to a non-linear second order positive
  feedback between the demographic growth and
  technological development
• Technological growth - increase in the carrying
  capacity of land for people - demographic growth
  - more people - more potential inventors -
  acceleration of technological growth -
  accelerating growth of the carrying capacity -
  the faster population growth - accelerating
  growth of the number of potential inventors -
  faster technological growth - hence, the faster
  growth of the Earth's carrying capacity for
  people, and so on
• Feed or Feedback, by A. Duncan Brown
• Positive loop between agriculture and population

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Example permafrost melting

• From U of Michigan project
• http//sitemaker.umich.edu/section2_group1/arctic_
  issues__permafrost
• The Terrestrial Carbon Cycle Climate Feedback

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Permafrost
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Details

• Warmer temperatures in the Artic have begun to
  thaw the arctic permafrost, a layer of soil that
  has been frozen since before the last ice age
• It contains frozen organic matter that has been
  preserved by the ice, historically making the
  permafrost layer a carbon sink that contains 14
  of the total carbon in the worlds soils
  (Christiansen 1995). A recent estimate suggests
  that if all of the carbon stored in permafrost
  were released into the atmosphere, the CO2 levels
  in the atmosphere would double
• The warmer than average temperatures recorded in
  this region in the last couple of decades have
  been indirectly causing the permafrost to change
  from a CO2 sink to a CO2 source (Oechel 1993) and
  has increased methane emissions as well
  (Christiansen 1995)
• This is being directly caused by an increase in
  soil drainage and aeration from temperature
  increases (PBS 2004)
• The effect of photosynthesis as a stabilizing
  factor in the process, through the increased
  exposure of vegetation to the atmosphere, is not
  expected to reach the levels CO2 out gassing any
  time soon, so the thawing of this layer has
  created a positive feedback loop known as the
  Terrestrial Carbon Cycle Climate Feedback (Oechel
  1993)

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Impact

• As this cycle feeds into itself, the thawing of
  the permafrost layer becomes an even greater
  issue.
• Much of the infrastructure of Alaska is built on
  this ancient permafrost and now that it is
  thawing, the water is starting to drain away and
  the ground is subsiding, causing once solid
  structures such as roads and buildings to crack
  and lean.
• This problem has become more wide spread and a
  greater concern throughout the Arctic as time has
  progressed (Armstrong 2003).
• Permafrost thawing and longer warmer seasons
  allows water that was previously contained to
  flow away and more evaporation throughout the
  year.
• The thawing is literally uncorking lakes so
  that the water is flowing out of Alaska and into
  the open oceans (Riordan 2006).
• 15 of the surface water in Alaska has been lost
  to this outflow in the last 50 years (PBS 2004).

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Couple of examples in biology

• Contractions in childbirth
• When a contraction occurs, oxytocin (a hormone)
  is released into the body, which stimulates
  further contractions, resulting in contractions
  increasing in amplitude and frequency
• Blood clotting
• The loop is initiated when injured tissue
  releases signal chemicals which activate
  platelets in the blood.
• An activated platelet releases chemicals which
  activate more platelets, causing a rapid cascade
  and the formation of a blood clot

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More examples

• So-called vicious cycles poverty, hunger, debt
• Converse virtuous cycles education,
  agricultural productivity, clean water, health,
  money
• Hyperbolic or exponential growth (second order
  behavior) is often driven by positive feedback
• Many examples in biology and population

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Negative feedback
F-
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Negative feedback

• System tending toward equilibrium
• In biology, we often use the term homeostasis
• Perturbations to the system are counteracted by
  the systems response
• Thermostats in machine and animal
• Many biological and ecological processes, because
  nature tends to self-regulate or react to
  oppose factors that destabilize the system
• And thats a very good thing

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Negative feedback
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More on negative feedback

• In biology

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Recognizing negative feedback

• Nature responds often cited for human induced
  change that is counteracted by environmental
  systems
• Often linked to unintended consequences